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Artykuły w czasopismach na temat „Odd parity path decomposition”

Autor: Grafiati

Data publikacji: 3 czerwca 2025

Data aktualizacji: 31 lipca 2025

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1

Petruševski, Mirko, and Riste Škrekovski. "Coverability of Graphs by Parity Regular Subgraphs." Mathematics 9, no. 2 (2021): 182. http://dx.doi.org/10.3390/math9020182.

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A graph is even (resp. odd) if all its vertex degrees are even (resp. odd). We consider edge coverings by prescribed number of even and/or odd subgraphs. In view of the 8-Flow Theorem, a graph admits a covering by three even subgraphs if and only if it is bridgeless. Coverability by three odd subgraphs has been characterized recently [Petruševski, M.; Škrekovski, R. Coverability of graph by three odd subgraphs. J. Graph Theory 2019, 92, 304–321]. It is not hard to argue that every acyclic graph can be decomposed into two odd subgraphs, which implies that every graph admits a decomposition into

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2

M., Sudha. "ARITHMETIC ODD DECOMPOSITION OF GRAPHS." Journal of Applied Mathematics and Statistical Analysis 4, no. 1 (2023): 8–13. https://doi.org/10.5281/zenodo.7817544.

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<em>The most important area in graph theory is graph decomposition [10]. Graph decomposition was first introduced by the mathematician Konig in 1960.Graph decomposition usually means collection of edge disjoint subgraphs such that each edge is appropriate to accurately unique. If every contains a trail or a cycle formerly we usually named it as path decomposition or cycle decomposition [1,6,9]. N. Gnana Dhas and J. Paul Raj Joseph [7] modified Ascending Subgraph Decomposition and introduced the concept known as Continous Monotonic Decomposition of graphs for connected graphs. An essential and

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3

de Souza, Jeferson, Saulo Pomponet Oliveira, and Francisco José Fonseca Ferreira. "Using parity decomposition for interpreting magnetic anomalies from dikes having arbitrary dip angles, induced and remanent magnetization." GEOPHYSICS 85, no. 3 (2020): J51—J58. http://dx.doi.org/10.1190/geo2019-0225.1.

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We have developed a technique to reconstruct the magnetic anomaly due to a dike in a way that the effect of magnetization direction is removed, resulting in a new totally symmetric anomaly. The reconstruction algorithm is easy to implement and could avoid the need of reduction to the pole at a low computational cost. The method is based on the decomposition of the function representing magnetic anomalies due to dikes in its even and odd parts. After applying a Hilbert transform to the odd components, we reconstruct the signal by a weighted average of the even part and the Hilbert-transformed o

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4

Prabhu, A., A. Brandenburg, M. J. Käpylä, and A. Lagg. "Helicity proxies from linear polarisation of solar active regions." Astronomy & Astrophysics 641 (September 2020): A46. http://dx.doi.org/10.1051/0004-6361/202037614.

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Context. The α effect is believed to play a key role in the generation of the solar magnetic field. A fundamental test for its significance in the solar dynamo is to look for magnetic helicity of opposite signs both between the two hemispheres as well as between small and large scales. However, measuring magnetic helicity is compromised by the inability to fully infer the magnetic field vector from observations of solar spectra, caused by what is known as the π ambiguity of spectropolarimetric observations. Aims. We decompose linear polarisation into parity-even and parity-odd E and B polarisa

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Kovács, Gergely, Benedek Nagy, Gergely Stomfai, Neşet Deniz Turgay, and Béla Vizvári. "Discrete Optimization: The Case of Generalized BCC Lattice." Mathematics 9, no. 3 (2021): 208. http://dx.doi.org/10.3390/math9030208.

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Recently, operations research, especially linear integer-programming, is used in various grids to find optimal paths and, based on that, digital distance. The 4 and higher-dimensional body-centered-cubic grids is the nD (n≥4) equivalent of the 3D body-centered cubic grid, a well-known grid from solid state physics. These grids consist of integer points such that the parity of all coordinates are the same: either all coordinates are odd or even. A popular type digital distance, the chamfer distance, is used which is based on chamfer paths. There are two types of neighbors (closest same parity a

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6

KAUFMANN, RALPH M. "PATH SPACE DECOMPOSITIONS FOR THE VIRASORO ALGEBRA AND ITS VERMA MODULES." International Journal of Modern Physics A 10, no. 07 (1995): 943–61. http://dx.doi.org/10.1142/s0217751x95000462.

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Starting from a detailed analysis of the structure of path spaces of the [Formula: see text] fusion graphs and the corresponding irreducible Virasoro algebra quotients V(c, h) for the (2, q odd) models, we introduce the notion of an admissible path space representation. The path spaces [Formula: see text] over the [Formula: see text] graphs are isomorphic to the path spaces over Coxeter A graphs that appear in FB models. We give explicit construction algorithms for admissible representations. From the finite-dimensional results of these algorithms we derive a decomposition of V(c, h) into its

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7

KANG, ROSS J., and FRANÇOIS PIROT. "Distance Colouring Without One Cycle Length." Combinatorics, Probability and Computing 27, no. 5 (2018): 794–807. http://dx.doi.org/10.1017/s0963548318000068.

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We consider distance colourings in graphs of maximum degree at most d and how excluding one fixed cycle of length ℓ affects the number of colours required as d → ∞. For vertex-colouring and t ⩾ 1, if any two distinct vertices connected by a path of at most t edges are required to be coloured differently, then a reduction by a logarithmic (in d) factor against the trivial bound O(dt) can be obtained by excluding an odd cycle length ℓ ⩾ 3t if t is odd or by excluding an even cycle length ℓ ⩾ 2t + 2. For edge-colouring and t ⩾ 2, if any two distinct edges connected by a path of fewer than t edges

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8

CHRISMAN, MICAH WHITNEY, and VASSILY OLEGOVICH MANTUROV. "PARITY AND EXOTIC COMBINATORIAL FORMULAE FOR FINITE-TYPE INVARIANTS OF VIRTUAL KNOTS." Journal of Knot Theory and Its Ramifications 21, no. 13 (2012): 1240001. http://dx.doi.org/10.1142/s0218216512400019.

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The present paper produces examples of Gauss diagram formulae for virtual knot invariants which have no analogue in the classical knot case. These combinatorial formulae contain additional information about how a subdiagram is embedded in a virtual knot diagram. The additional information comes from the second author's recently discovered notion of parity. For a parity of flat virtual knots, the new combinatorial formulae are Kauffman finite-type invariants. However, many of the combinatorial formulae possess exotic properties. It is shown that there exists an integer-valued virtualization inv

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9

Santoso, Jaya. "On the Chromatic Number of Cycle Books Graph." Compiler 14, no. 1 (2025): 27. https://doi.org/10.28989/compiler.v14i1.2930.

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Graph coloring is a fundamental topic in graph theory, with various applications in scheduling, networking, and optimization problems. In this study, we investigate the chromatic number of the cycle books graph , a structured graph formed by attaching multiple cycles to a common path . We establish that the chromatic number of depends on the parity of . Specifically, we prove that if is even, the chromatic number is , while if is odd, the chromatic number is . These results provide a deeper understanding of coloring properties in book-like graphs and contribute to the broader study of chromati

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10

Nosov, A. P., A. A. Akhrem, and V. Z. Rakhmankulov. "Efficiency Analysis of OLAP-data Hypercube Decomposition for Exponential Computational Complexity Methods." Mathematics and Mathematical Modeling, no. 3 (December 9, 2021): 29–45. http://dx.doi.org/10.24108/mathm.0321.0000258.

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The paper studies problems of reduction (decomposition) of OLAP-hypercube multidimensional data models. When decomposing large hyper-cubes of multidimensional data into sub-cube components the goal is to increase the computational performance of analytical OLAP systems, which is related to decreasing computational complexity of reduction methods for solving OLAP-data analysis problems with respect to the computational complexity of non-reduction methods, applied to data directly all over the hypercube. The paper formalizes the concepts of reduction and non-reduction methods and gives a definit

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11

Zheng, W., F. M. Flocke, G. S. Tyndall, et al. "Characterization of a thermal decomposition chemical ionization mass spectrometer for the measurement of peroxy acyl nitrates (PANs) in the atmosphere." Atmospheric Chemistry and Physics Discussions 11, no. 3 (2011): 8461–513. http://dx.doi.org/10.5194/acpd-11-8461-2011.

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Abstract. This paper presents a detailed laboratory characterization of a thermal dissociation ionization mass spectrometer (TD-CIMS) for the atmospheric measurement of Peroxyacetyl nitrate (PAN) and its homologues. PANs are efficiently dissociated in a heated inlet tube and the resulting peroxy acyl radicals are reacted with I– ions in a flow tube. The CIMS detects the corresponding carboxylate ions to give a specific and quantitative measurement of each PAN species. PAN, peroxypropionyl nitrate (PPN), peroxyisobutyryl nitrate (PiBN), peroxy-n-butyryl nitrate (PnBN), peroxyacryloyl nitrate (A

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12

Zheng, W., F. M. Flocke, G. S. Tyndall, et al. "Characterization of a thermal decomposition chemical ionization mass spectrometer for the measurement of peroxy acyl nitrates (PANs) in the atmosphere." Atmospheric Chemistry and Physics 11, no. 13 (2011): 6529–47. http://dx.doi.org/10.5194/acp-11-6529-2011.

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Abstract. This paper presents a detailed laboratory characterization of a thermal dissociation chemical ionization mass spectrometer (TD-CIMS) for the atmospheric measurement of Peroxyacetyl nitrate (PAN) and its homologues (PANs). PANs are efficiently dissociated in a heated inlet and the resulting peroxy acyl radicals are reacted with I− ions in a flow tube. The mass spectrometer detects the corresponding carboxylate ions. PAN, peroxypropionyl nitrate (PPN), peroxyisobutyryl nitrate (PiBN), peroxy-n-butyryl nitrate (PnBN), peroxyacryloyl nitrate (APAN), peroxycrotonyl nitrates (CPAN) and per

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13

Conrado, Giovanna Kobus, Amir Kafshdar Goharshady, and Chun Kit Lam. "The Bounded Pathwidth of Control-Flow Graphs." Proceedings of the ACM on Programming Languages 7, OOPSLA2 (2023): 292–317. http://dx.doi.org/10.1145/3622807.

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Pathwidth and treewidth are standard and well-studied graph sparsity parameters which intuitively model the degree to which a given graph resembles a path or a tree, respectively. It is well-known that the control-flow graphs of structured goto-free programs have a tree-like shape and bounded treewidth. This fact has been exploited to design considerably more efficient algorithms for a wide variety of static analysis and compiler optimization problems, such as register allocation, µ-calculus model-checking and parity games, data-flow analysis, cache management, and liftetime-optimal redundancy

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14

K., Nagarajan, Nagarajan A., and Sahul Hamid I. "Equiparity Path Decomposition Number of a Graph." April 15, 2009. https://doi.org/10.5281/zenodo.809368.

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Here we impose parity condition on lengths of the paths and define an equiparity path cover as follows. An equiparity path decomposition of a graph <em>G</em> is a path cover of <em>G</em> such that the lengths of all the paths in have the same parity. The minimum cardinality of a equiparity path decomposition of <em>G</em> is called the equiparity path decomposition number of<em> G</em> and is denoted by <em>xp (G)</em>.

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15

Rostami, Habib, Nitay Ben-Shachar, Sergej Moroz, and Johannes Hofmann. "Magnetic field suppression of tomographic electron transport." Physical Review B 111, no. 15 (2025). https://doi.org/10.1103/physrevb.111.155434.

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Degenerate two-dimensional electron liquids are theoretically established to possess two vastly distinct collisional electron mean free paths, where even-parity deformations of the Fermi surface are hydrodynamic with a short collisional mean free path but odd-parity deformations remain near ballistic (known as the “tomographic” transport regime). Predicted signatures of this regime rely on the scaling of observables with temperature or device dimension, both of which are difficult to establish with certainty. Here, we consider magnetotransport in a minimal model of tomographic electrons and sh

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16

Kotlar, Daniel. "Parity Types, Cycle Structures and Autotopisms of Latin Squares." Electronic Journal of Combinatorics 19, no. 3 (2012). http://dx.doi.org/10.37236/2538.

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The parity type of a Latin square is defined in terms of the numbers of even and odd rows and columns. It is related to an Alon-Tarsi-like conjecture that applies to Latin squares of odd order. Parity types are used to derive upper bounds for the size of autotopy groups. A new algorithm for finding the autotopy group of a Latin square, based on the cycle decomposition of its rows, is presented, and upper bounds for the size of autotopy groups are derived from it.

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17

Hamid, Ismail Sahul, and Mayamma Joseph. "A Variation of Decomposition Under a Length Constraint." April 27, 2011. https://doi.org/10.5281/zenodo.8723.

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Introducing and initiating a study of a new variation of decomposition namely equiparity induced path decomposition of a graph which is defined to be a decomposition in which all the members are induced paths having same parity.

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18

Martini, Riccardo, Gregorio Paci, and Dario Sauro. "Covariant spin-parity decomposition of the Torsion and Path Integrals." Classical and Quantum Gravity, August 15, 2023. http://dx.doi.org/10.1088/1361-6382/acf08b.

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Abstract We propose a functional measure over the torsion tensor. We discuss two completely equivalent choices for the Wheeler-DeWitt supermetric for this field, the first one is based on its algebraic decomposition and the other is inspired by teleparallel theories of gravity. The measure is formally defined by requiring the normalization of the Gaussian integral. To achieve such a result we split the torsion tensor into its spin-parity eigenstates by constructing a new, York-like, decomposition. Of course, such a decomposition has a wider range of applicability to any kind of tensor sharing

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19

Jiménez, Andrea, and Yoshiko Wakabayashi. "On path-cycle decompositions of triangle-free graphs." Discrete Mathematics & Theoretical Computer Science Vol. 19 no. 3, Graph Theory (2017). https://doi.org/10.23638/dmtcs-19-3-7.

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In this work, we study conditions for the existence of length-constrained path-cycle decompositions, that is, partitions of the edge set of a graph into paths and cycles of a given minimum length. Our main contribution is the characterization of the class of all triangle-free graphs with odd distance at least $3$ that admit a path-cycle decomposition with elements of length at least $4$. As a consequence, it follows that Gallai's conjecture on path decomposition holds in a broad class of sparse graphs.

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20

De Vas Gunasekara, Ajani, and Alice Devillers. "Transitive path decompositions of Cartesian products of complete graphs." Designs, Codes and Cryptography, October 3, 2024. http://dx.doi.org/10.1007/s10623-024-01493-9.

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AbstractAn H-decomposition of a graph $$\Gamma $$ Γ is a partition of its edge set into subgraphs isomorphic to H. A transitive decomposition is a special kind of H-decomposition that is highly symmetrical in the sense that the subgraphs (copies of H) are preserved and transitively permuted by a group of automorphisms of $$\Gamma $$ Γ . This paper concerns transitive H-decompositions of the graph $$K_n \Box K_n$$ K n □ K n where H is a path. When n is an odd prime, we present a construction for a transitive path decomposition where the paths in the decomposition are considerably large compared

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21

Larue, Rémy, Jérémie Quevillon, and Roman Zwicky. "Trace anomaly of weyl fermions via the path integral." Journal of High Energy Physics 2023, no. 12 (2023). http://dx.doi.org/10.1007/jhep12(2023)064.

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Abstract We compute the trace, diffeomorphism and Lorentz anomalies of a free Weyl fermion in a gravitational background field by path integral methods. This is achieved by regularising the variation of the determinant of the Weyl operator building on earlier work by Leutwyler. The trace anomaly is found to be one half of the one of a Dirac fermion. Most importantly we establish that the potential parity-odd curvature term $$ R\overset{\sim }{R} $$ R R ~ , corresponding to the Pontryagin density, vanishes. This is to the contrary of some recent findings in the literature which gave rise to a c

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22

Chen, Ricky Xiaofeng. "A New Bijection Between RNA Secondary Structures and Plane Trees and its Consequences." Electronic Journal of Combinatorics 26, no. 4 (2019). http://dx.doi.org/10.37236/8540.

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In this paper, we first present a new bijection between RNA secondary structures and plane trees. Combined with the Schmitt-Waterman bijection between these objects, we then obtain a bijection on plane trees that relates the horizontal fiber decomposition associated to internal vertices to the degrees of odd-level vertices while the vertical path decomposition associated to leaves is related to the degrees of even-level vertices. To the best of our knowledge, only the former relation (i.e., horizontal vs odd-level) due to Deutsch is known. As a consequence, we obtain enumeration results for va

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23

Stefanyszyn, David, Xi Tong, and Yuhang Zhu. "Cosmological correlators through the looking glass: reality, parity, and factorisation." Journal of High Energy Physics 2024, no. 5 (2024). http://dx.doi.org/10.1007/jhep05(2024)196.

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Abstract We consider the evolution of quantum fields during inflation, and show that the total-energy singularities appearing in the perturbative expansion of the late-time Wavefunction of the Universe are purely real when the external states are massless scalars and massless gravitons. Our proof relies on the tree-level approximation, Bunch-Davies initial conditions, and exact scale invariance (IR-convergence), but without any assumptions on invariance under de Sitter boosts. We consider all n-point functions and allow for the exchange of additional states of any mass and integer spin. Our pr

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24

Corianò, Claudio, Stefano Lionetti, and Matteo Maria Maglio. "Parity-odd 3-point functions from CFT in momentum space and the chiral anomaly." European Physical Journal C 83, no. 6 (2023). http://dx.doi.org/10.1140/epjc/s10052-023-11661-1.

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AbstractWe illustrate how the Conformal Ward Identities (CWI) in momentum space for parity-odd correlators determine the structure of a chiral anomaly interaction, taking the example of the VVA (vector/vector/axial-vector) and AAA correlators in momentum space. Only the conservation and the anomalous WIs, together with the Bose symmetry, are imposed from the outset for the determination of the correlators. We use a longitudinal/transverse decomposition of tensor structures and form factors. The longitudinal (L) component is fixed by the anomaly content and the anomaly pole, while in the transv

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25

Wang, Xiumei, Cheng He, and Yixun Lin. "Removable edges in near-bricks." Discrete Mathematics & Theoretical Computer Science Vol. 15 no. 2, Graph Theory (2013). http://dx.doi.org/10.46298/dmtcs.600.

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Graph Theory International audience For a brick apart from a few small graphs, Lovász (1987) proposed a conjecture on the existence of an edge whose deletion results in a graph with only one brick in its tight cut decomposition. Carvalho, Lucchesi, and Murty (2002) confirmed this conjecture by showing the existence of such two edges. This paper generalizes the result obtained by Carvalho et al. to the case of irreducible near-brick, where a graph is irreducible if it contains no induced odd path of length 3 or more. Meanwhile, a lower bound on the number of removable edges of matching-covered

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26

Kumano, Shunzo, and Qin-Tao Song. "Transverse-momentum-dependent parton distribution functions for spin-1 hadrons." SciPost Physics Proceedings, no. 8 (July 14, 2022). http://dx.doi.org/10.21468/scipostphysproc.8.174.

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We show transverse-momentum-dependent parton distribution functions (TMDs) for spin-1 hadrons including twist-3 and 4 functions by taking the decomposition of a quark correlation function in the Lorentz-invariant way with the conditions of Hermiticity and parity invariance. We found 30 new TMDs in the tensor-polarized spin-1 hadron at twists 3 and 4 in addition to 10 TMDs at twist 2. Since time-reversal-odd terms of the collinear correlation function should vanish after integrals over the partonic transverse momentum, we obtained new sum rules for the time-reversal-odd structure functions, {\i

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27

T., N. Janakiraman, and Janet Lourds Rani J. "Delay Preserving Substructures in Wireless Networks Using Edge Difference between a Graph and its Square Graph." June 21, 2008. https://doi.org/10.5281/zenodo.1072471.

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In practice, wireless networks has the property that the signal strength attenuates with respect to the distance from the base station, it could be better if the nodes at two hop away are considered for better quality of service. In this paper, we propose a procedure to identify delay preserving substructures for a given wireless ad-hoc network using a new graph operation G 2 – E (G) = G* (Edge difference of square graph of a given graph and the original graph). This operation helps to analyze some induced substructures, which preserve delay in communication among them. This operation G* on a

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28

Shen, Shiwen, Wei Zhang, and Lubing Shao. "Effective Hamiltonian of magnetic moments in proximity with an s-wave superconductor." Journal of Physics D: Applied Physics, August 2, 2023. http://dx.doi.org/10.1088/1361-6463/acec82.

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Abstract In this paper, we consider two magnetic moments in proximity with an $ s $-wave superconductor, where each magnetic moment has an internal energy level. The effective Hamiltonian of the two magnetic moments is derived in this paper by path integral in the weak coupling limit. Interestingly, there are four new terms by the proximity effect, including the Ruderman-Kittel-Kasuya-Yosida interaction, the hopping term, the cross and on-site superconducting pairing potentials. Additionally, since the parity of electrons is conserved, the Hilbert space is split into two subspaces of even and

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29

Jr., Victor B. Calinao, Edwin Sybingco, Argel A. Bandala, and Lawrence Materum. "Energy and Nvidia Sionna-Based Signal Integrity: Selection Design for Off-the-Shelf Synthetic Aperture Radar-Capable Unmanned Aerial Vehicles." Journal of Communications, 2023, 29–35. http://dx.doi.org/10.12720/jcm.18.1.29-35.

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This paper presents the relationship between energy and signal integrity of Unmanned Aerial Vehicles (UAVs) with Synthetic Aperture Radar (SAR) capabilities for a more informed off-the-shelf selection design. The energy is expressed in the UAV and SAR power consumption, whereas signal integrity is expressed in Bit-Error Rate (BER). Low-end, mid-end, and highend—categorized in terms of their market cost—commercial UAVs and SAR modules were considered. The energy relations are based on the UAV flight path and power ratings. The signal processing and decomposition of the reconstructed objects for

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Blauth, Jannis, Nathan Klein, and Martin Nägele. "A better-than-1.6-approximation for prize-collecting TSP." Mathematical Programming, May 12, 2025. https://doi.org/10.1007/s10107-025-02221-4.

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Abstract Prize-Collecting TSP is a variant of the traveling salesperson problem where one may drop vertices from the tour at the cost of vertex-dependent penalties. The quality of a solution is then measured by adding the length of the tour and the sum of all penalties of vertices that are not visited. We present a polynomial-time approximation algorithm with an approximation guarantee slightly below 1.6, where the guarantee is with respect to the natural linear programming relaxation of the problem. This improves upon the previous best-known approximation ratio of 1.774. Our approach is based

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Henry, Garrett. "0027 | Metric Dimension in fuzzy(neutrosophic) Graphs-VI." November 22, 2021. https://doi.org/10.20944/preprints202111.0142.v6.

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New notion of dimension as set, as two optimal numbers including metric number, dimension number and as optimal set are introduced in individual framework and in formation of family. Behaviors of twin and antipodal are explored in fuzzy(neutrosophic) graphs. Fuzzy(neutrosophic) graphs, under conditions, fixed-edges, fixed-vertex and strong fixed-vertex are studied. Some classes as path, cycle, complete, strong, t-partite, bipartite, star and wheel in the formation of individual case and in the case, they form a family are studied in the term of dimension. Fuzzification (neutrosofication) of tw

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Henry, Garrett. "0030 | Metric Dimension in fuzzy(neutrosophic) Graphs #9." November 25, 2021. https://doi.org/10.5281/zenodo.6319873.

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New notion of dimension as set, as two optimal numbers including metric number, dimension number and as optimal set are introduced in individual framework and in formation of family. Behaviors of twin and antipodal are explored in fuzzy(neutrosophic) graphs. Fuzzy(neutrosophic) graphs, under conditions, fixed-edges, fixed-vertex and strong fixed-vertex are studied. Some classes as path, cycle, complete, strong, t-partite, bipartite, star and wheel in the formation of individual case and in the case, they form a family are studied in the term of dimension. Fuzzification (neutrosofication) of tw

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Henry, Garrett. "0028 | Metric Dimension in fuzzy(neutrosophic) Graphs-VII." November 24, 2021. https://doi.org/10.5281/zenodo.6319835.

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New notion of dimension as set, as two optimal numbers including metric number, dimension number and as optimal set are introduced in individual framework and in formation of family. Behaviors of twin and antipodal are explored in fuzzy(neutrosophic) graphs. Fuzzy(neutrosophic) graphs, under conditions, fixed-edges, fixed-vertex and strong fixed-vertex are studied. Some classes as path, cycle, complete, strong, t-partite, bipartite, star and wheel in the formation of individual case and in the case, they form a family are studied in the term of dimension. Fuzzification (neutrosofication) of tw

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Henry, Garrett. "0029 | Metric Dimension in fuzzy(neutrosophic) Graphs #8." November 25, 2021. https://doi.org/10.5281/zenodo.6319838.

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New notion of dimension as set, as two optimal numbers including metric number, dimension number and as optimal set are introduced in individual framework and in formation of family. Behaviors of twin and antipodal are explored in fuzzy(neutrosophic) graphs. Fuzzy(neutrosophic) graphs, under conditions, fixed-edges, fixed-vertex and strong fixed-vertex are studied. Some classes as path, cycle, complete, strong, t-partite, bipartite, star and wheel in the formation of individual case and in the case, they form a family are studied in the term of dimension. Fuzzification (neutrosofication) of tw

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Henry, Garrett. "0031 | Metric Dimension in fuzzy(neutrosophic) Graphs #10." November 26, 2021. https://doi.org/10.5281/zenodo.6319877.

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New notion of dimension as set, as two optimal numbers including metric number, dimension number and as optimal set are introduced in individual framework and in formation of family. Behaviors of twin and antipodal are explored in fuzzy(neutrosophic) graphs. Fuzzy(neutrosophic) graphs, under conditions, fixed-edges, fixed-vertex and strong fixed-vertex are studied. Some classes as path, cycle, complete, strong, t-partite, bipartite, star and wheel in the formation of individual case and in the case, they form a family are studied in the term of dimension. Fuzzification (neutrosofication) of tw

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Henry, Garrett. "0032 | Metric Dimension in fuzzy(neutrosophic) Graphs #11." March 1, 2022. https://doi.org/10.5281/zenodo.6319883.

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New notion of dimension as set, as two optimal numbers including metric number, dimension number and as optimal set are introduced in individual framework and in formation of family. Behaviors of twin and antipodal are explored in fuzzy(neutrosophic) graphs. Fuzzy(neutrosophic) graphs, under conditions, fixed-edges, fixed-vertex and strong fixed-vertex are studied. Some classes as path, cycle, complete, strong, t-partite, bipartite, star and wheel in the formation of individual case and in the case, they form a family are studied in the term of dimension. Fuzzification (neutrosofication) of tw

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Henry, Garrett. "0033 | Metric Dimension in fuzzy(neutrosophic) Graphs #12." December 7, 2021. https://doi.org/10.5281/zenodo.6319886.

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New notion of dimension as set, as two optimal numbers including metric number, dimension number and as optimal set are introduced in individual framework and in formation of family. Behaviors of twin and antipodal are explored in fuzzy(neutrosophic) graphs. Fuzzy(neutrosophic) graphs, under conditions, fixed-edges, fixed-vertex and strong fixed-vertex are studied. Some classes as path, cycle, complete, strong, t-partite, bipartite, star and wheel in the formation of individual case and in the case, they form a family are studied in the term of dimension. Fuzzification (neutrosofication) of tw

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Shichi, Masahiro, Mikio Yasutake, and Kazuchika Ohta. "Discotic liquid crystals of transition metal complexes 59: Parity effect of the number of d-electrons on the columnar mesomorphism and homeotropic alignment of 1,4-diazatriphenylenocyaninato metal(II) complexes." Journal of Porphyrins and Phthalocyanines, June 23, 2021, A—O. http://dx.doi.org/10.1142/s1088424621500668.

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Twenty super-discotic liquid crystals based on a largely expanded [Formula: see text]-conjugated macrocycle of 1,4-diazatriphenylenocyaninato metal(II) complex, (abbreviated as (C[Formula: see text]O)[Formula: see text]TzM: M = Co (1), Ni (2), Cu (3), Zn (4); [Formula: see text] = 8 (a), 10 (b), 12 (c), 14(d), 16 (e)) were synthesized in order to investigate their mesomorphism and homeotropic alignment properties by using polarization microscopic observations, differential calorimetry, thermogravimetry, and temperature-variable X-ray diffraction. As a result, the (C[Formula: see text]O)[Formul

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Henry, Garrett. "New Ideas On Super Decompensation By Hyper Decompress Of Eulerian-Path-Decomposition In Cancer's Recognition With (Neutrosophic) SuperHyperGraph." April 11, 2023. https://doi.org/10.5281/zenodo.7819579.

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\documentclass[10pt,letterpaper]{article} \usepackage[top=0.85in,left=2.79in,footskip=0.79in,marginparwidth=2in]{geometry} \usepackage{amsmath, amsthm, amscd, amsfonts, amssymb, graphicx, tikz, color} \usepackage[bookmarksnumbered, colorlinks, plainpages]{hyperref} % use Unicode characters - try changing the option if you run into troubles with special characters (e.g. umlauts) \usepackage[utf8]{inputenc} % clean citations \usepackage{cite} % hyperref makes references clicky. use \url{www.example.com} or \href{www.example.com}{description} to add a clicky url \usepackage{nameref,hyperref} % li

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Henry, Garrett. "New Ideas In Recognition of Cancer And Neutrosophic SuperHyperGraph By Eulerian-Path-Decomposition As Hyper Decompress On Super Decompensation." April 11, 2023. https://doi.org/10.5281/zenodo.7819531.

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\documentclass[10pt,letterpaper]{article} \usepackage[top=0.85in,left=2.79in,footskip=0.79in,marginparwidth=2in]{geometry} \usepackage{amsmath, amsthm, amscd, amsfonts, amssymb, graphicx, tikz, color} \usepackage[bookmarksnumbered, colorlinks, plainpages]{hyperref} % use Unicode characters - try changing the option if you run into troubles with special characters (e.g. umlauts) \usepackage[utf8]{inputenc} % clean citations \usepackage{cite} % hyperref makes references clicky. use \url{www.example.com} or \href{www.example.com}{description} to add a clicky url \usepackage{nameref,hyperref} % li

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Martini, Riccardo, Gregorio Paci, and Dario Sauro. "Radiative corrections to the R and R2 invariants from torsion fluctuations on maximally symmetric spaces." Journal of High Energy Physics 2024, no. 12 (2024). https://doi.org/10.1007/jhep12(2024)138.

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Abstract We derive the runnings of the R and R2 operators that stem from integrating out quantum torsion fluctuations on a maximally symmetric Euclidean background, while treating the metric as a classical field. Our analysis is performed in a manifestly covariant way, exploiting both the recently-introduced spin-parity decomposition of torsion perturbations and the heat kernel technique. The Lagrangian we start with is the most general one for 1-loop computations on maximally symmetric backgrounds involving kinetic terms and couplings to the scalar curvature that is compatible with a gauge-li

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Henry, Garrett. "New Ideas On Super Decompensation By Hyper Decompress Of Eulerian-Type-Path-Decomposition In Cancer's Recognition With (Neutrosophic) SuperHyperGraph." April 18, 2023. https://doi.org/10.5281/zenodo.7840206.

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248 Henry Garrett, “New Ideas On Super Decompensation By Hyper Decompress Of Eulerian-Type-Path-Decomposition In Cancer's Recognition With (Neutrosophic) SuperHyperGraph”, Zenodo 2023, (doi: 10.5281/zenodo.7840206). @ResearchGate: https://www.researchgate.net/publication/- @Scribd: https://www.scribd.com/document/- @ZENODO_ORG: https://zenodo.org/record/7840206 @academia: https://www.academia.edu/-   \documentclass[10pt,letterpaper]{article} \usepackage[top=0.85in,left=2.79in,footskip=0.79in,marginparwidth=2in]{geometry} \usepackage{amsmath, amsthm, amscd, amsfonts, amssym

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Henry, Garrett. "New Ideas In Recognition of Cancer And Neutrosophic SuperHyperGraph By Eulerian-Type-Path-Decomposition As Hyper Decompress On Super Decompensation." April 18, 2023. https://doi.org/10.5281/zenodo.7839333.

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\documentclass[10pt,letterpaper]{article} \usepackage[top=0.85in,left=2.79in,footskip=0.79in,marginparwidth=2in]{geometry} \usepackage{amsmath, amsthm, amscd, amsfonts, amssymb, graphicx, tikz, color} \usepackage[bookmarksnumbered, colorlinks, plainpages]{hyperref} % use Unicode characters - try changing the option if you run into troubles with special characters (e.g. umlauts) \usepackage[utf8]{inputenc} % clean citations \usepackage{cite} % hyperref makes references clicky. use \url{www.example.com} or \href{www.example.com}{description} to add a clicky url \usepackage{nameref,hyperref} % li

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Henry, Garrett. "0044 | Co-Neighborhood in Neutrosophic Graphs." February 1, 2022. https://doi.org/10.13140/RG.2.2.17687.44964.

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New setting is introduced to study the co-neighborhood. co-neighborhood is about a set of vertices which are applied into the setting of neutrosophic graphs. Neighborhood has the key role to define this notion. Also, neighborhood is defined based on strong edges. Strong edge gets a framework as neighborhood and after that, too close vertices have key role to define co-neighborhood based on strong edges. The structure of set is studied and general results are obtained. Also, some classes of neutrosophic graphs excluding empty, complete bipartite, bipartite and wheel and containing odd-path-neut

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Dujmović, Vida, Louis Esperet, Gwenaël Joret, Bartosz Walczak, and David Wood. "Planar graphs have bounded nonrepetitive chromatic number." Advances in Combinatorics, March 6, 2020. http://dx.doi.org/10.19086/aic.12100.

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The following seemingly simple question with surprisingly many connections to various problems in computer science and mathematics can be traced back to the beginning of the 20th century to the work of [Axel Thue](https://en.wikipedia.org/wiki/Axel_Thue): How many colors are needed to color the positive integers in a way such that no two consecutive segments of the same length have the same color pattern? Clearly, at least three colors are needed: if there was such a coloring with two colors, then any two consecutive integers would have different colors (otherwise, we would get two consecutive

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Henry, Garrett. "0042 | Global Offensive Alliance in Strong Neutrosophic Graphs." January 21, 2022. https://doi.org/10.13140/RG.2.2.26541.20961.

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New setting is introduced to study the global offensive alliance. Global offensive alliance is about a set of vertices which are applied into the setting of neutrosophic graphs. Neighborhood has the key role to define this notion. Also, neighborhood is defined based on strong edges. Strong edge gets a framework as neighborhood and after that, too close vertices have key role to define global offensive alliance based on strong edges. The structure of set is studied and general results are obtained. Also, some classes of neutrosophic graphs containing complete, empty, path, cycle, star, and whee

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Henry, Garrett. "0042 | Global Offensive Alliance in Strong Neutrosophic Graphs." January 28, 2022. https://doi.org/10.5281/zenodo.6319972.

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New setting is introduced to study the global offensive alliance. Global offensive alliance is about a set of vertices which are applied into the setting of neutrosophic graphs. Neighborhood has the key role to define this notion. Also, neighborhood is defined based on strong edges. Strong edge gets a framework as neighborhood and after that, too close vertices have key role to define global offensive alliance based on strong edges. The structure of set is studied and general results are obtained. Also, some classes of neutrosophic graphs containing complete, empty, path, cycle, star, and whee

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Henry, Garrett. "New Ideas On Super Decompensation By Hyper Decompress Of Eulerian-Type-Cycle-Decomposition In Cancer's Recognition With (Neutrosophic) SuperHyperGraph." May 7, 2023. https://doi.org/10.5281/zenodo.7904401.

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260 Henry Garrett, “New Ideas On Super Decompensation By Hyper Decompress Of Eulerian-Type-Cycle-Decomposition In Cancer's Recognition With (Neutrosophic) SuperHyperGraph”, Zenodo 2023, (doi: 10.5281/zenodo.7904401). @ResearchGate: https://www.researchgate.net/publication/- @Scribd: https://www.scribd.com/document/- @ZENODO_ORG: https://zenodo.org/record/7904401 @academia: https://www.academia.edu/- \documentclass[10pt,letterpaper]{article} \usepackage[top=0.85in,left=2.79in,footskip=0.79in,marginparwidth=2in]{geometry} \usepackage{amsmath, amsthm, amscd, amsfonts, amssymb, gra

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Henry, Garrett. "New Ideas In Recognition of Cancer And Neutrosophic SuperHyperGraph By Eulerian-Type-Cycle-Decomposition As Hyper Decompress On Super Decompensation." May 7, 2023. https://doi.org/10.5281/zenodo.7904529.

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261 Henry Garrett, “New Ideas In Recognition of Cancer And Neutrosophic SuperHyperGraph By Eulerian-Type-Cycle-Decomposition As Hyper Decompress On Super Decompensation”, Zenodo 2023, (doi: 10.5281/zenodo.7904529). @ResearchGate: https://www.researchgate.net/publication/- @Scribd: https://www.scribd.com/document/- @ZENODO_ORG: https://zenodo.org/record/7904529 @academia: https://www.academia.edu/- \documentclass[10pt,letterpaper]{article} \usepackage[top=0.85in,left=2.79in,footskip=0.79in,marginparwidth=2in]{geometry} \usepackage{amsmath, amsthm, amscd, amsfonts, amssymb, graphicx,

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Henry, Garrett. "New Ideas On Super Decompensation By Hyper Decompress Of Eulerian-Cycle-Decomposition In Recognition of Cancer With (Neutrosophic) SuperHyperGraph." April 22, 2023. https://doi.org/10.5281/zenodo.7855637.

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254 Henry Garrett, “New Ideas On Super Decompensation By Hyper Decompress Of Eulerian-Cycle-Decomposition In Recognition of Cancer With (Neutrosophic) SuperHyperGraph”, Zenodo 2023, (doi: 10.5281/zenodo.7855637). @ResearchGate: https://www.researchgate.net/publication/- @Scribd: https://www.scribd.com/document/- @ZENODO_ORG: https://zenodo.org/record/7855637 @academia: https://www.academia.edu/-   \documentclass[10pt,letterpaper]{article} \usepackage[top=0.85in,left=2.79in,footskip=0.79in,marginparwidth=2in]{geometry} \usepackage{amsmath, amsthm, amscd, amsfonts, amssymb, grap

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