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Journal articles on the topic 'Extreme vertex'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Klavzar, Sandi, and Sara Zemljic. "On distances in Sierpiński graphs: Almost-extreme vertices and metric dimension." Applicable Analysis and Discrete Mathematics 7, no. 1 (2013): 72–82. http://dx.doi.org/10.2298/aadm130109001k.

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Sierpi?ski graphs Sn p form an extensively studied family of graphs of fractal nature applicable in topology, mathematics of the Tower of Hanoi, computer science, and elsewhere. An almost-extreme vertex of Sn p is introduced as a vertex that is either adjacent to an extreme vertex of Sn p or is incident to an edge between two subgraphs of Sn p isomorphic to Snp-1. Explicit formulas are given for the distance in Sn p between an arbitrary vertex and an almostextreme vertex. The formulas are applied to compute the total distance of almost-extreme vertices and to obtain the metric dimension of Sie

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2

Titus, P., and A. P. Santhakumaran. "Extreme Monophonic Graphs and Extreme Geodesic Graphs." Tamkang Journal of Mathematics 47, no. 4 (2016): 393–404. http://dx.doi.org/10.5556/j.tkjm.47.2016.2045.

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For a connected graph $G=(V,E)$ of order at least two, a chord of a path $P$ is an edge joining two non-adjacent vertices of $P$. A path $P$ is called a monophonic path if it is a chordless path. A monophonic set of $G$ is a set $S$ of vertices such that every vertex of $G$ lies on a monophonic path joining some pair of vertices in $S$. The monophonic number of $G$ is the minimum cardinality of its monophonic sets and is denoted by $m(G)$. A geodetic set of $G$ is a set $S$ of vertices such that every vertex of $G$ lies on a geodesic joining some pair of vertices in $S$. The geodetic number of

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SANTHAKUMARAN, A. P. "EXTREME STEINER GRAPHS." Discrete Mathematics, Algorithms and Applications 04, no. 02 (2012): 1250029. http://dx.doi.org/10.1142/s1793830912500292.

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For a connected graph G of order p ≥ 2 and a set W ⊆ V(G), a tree T contained in G is a Steiner tree with respect to W if T is a tree of minimum order with W ⊆ V(T). The set S(W) consists of all vertices in G that lie on some Steiner tree with respect to W. The set W is a Steiner set for G if S(W) = V(G). The Steiner number s(G) of G is the minimum cardinality of its Steiner sets and any Steiner set of cardinality s(G) is a minimum Steiner set of G. A geodetic set of G is a set S of vertices such that every vertex of G is contained in a geodesic joining some pair of vertices of S. The geodetic

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McKEE, TERRY A. "WHEN ALL MINIMAL VERTEX SEPARATORS INDUCE COMPLETE OR EDGELESS SUBGRAPHS." Discrete Mathematics, Algorithms and Applications 05, no. 03 (2013): 1350015. http://dx.doi.org/10.1142/s1793830913500158.

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The graphs in which every minimal vertex separator induces a complete or an edgeless subgraph are shown to be the edge sums of graphs of the two extreme types: (i) when every minimal vertex separator induces a complete subgraph — these are precisely the well-studied chordal graphs — and (ii) when every minimal vertex separator induces an edgeless subgraph — these have appeared in several recent papers.

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5

Woeginger, Gerhard J. "Finding the closest extreme vertex to a fixed point." Information Processing Letters 43, no. 3 (1992): 129–33. http://dx.doi.org/10.1016/0020-0190(92)90004-f.

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TANTAWY, S. F. "SOLVING A SPECIAL CLASS OF MULTIPLE OBJECTIVE LINEAR FRACTIONAL PROGRAMMING PROBLEMS." ANZIAM Journal 56, no. 1 (2014): 91–103. http://dx.doi.org/10.1017/s1446181114000200.

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AbstractIn this paper a feasible direction method is presented to find all efficient extreme points for a special class of multiple objective linear fractional programming problems, when all denominators are equal. This method is based on the conjugate gradient projection method, so that we start with a feasible point and then a sequence of feasible directions towards all efficient adjacent extremes of the problem can be generated. Since methods based on vertex information may encounter difficulties as the problem size increases, we expect that this method will be less sensitive to problem siz

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7

Febres. "A Space Decomposition-Based Deterministic Algorithm for Solving Linear Optimization Problems." Axioms 8, no. 3 (2019): 92. http://dx.doi.org/10.3390/axioms8030092.

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This document introduces a method to solve linear optimization problems. The method’s strategy is based on the bounding condition that each constraint exerts over the dimensions of the problem. The solution of a linear optimization problem is at the intersection of the constraints defining the extreme vertex. The method decomposes the n-dimensional linear problem into n-1 two-dimensional problems. After studying the role of constraints in these two-dimensional problems, we identify the constraints intersecting at the extreme vertex. We then formulate a linear equation system that directly lead

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8

Yang, Chenxu, Meng Ji, Kinkar Chandra Das, and Yaping Mao. "Extreme graphs on the Sombor indices." AIMS Mathematics 7, no. 10 (2022): 19126–46. http://dx.doi.org/10.3934/math.20221050.

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<abstract><p>Gutman proposed the concept of Sombor index. It is defined via the term $ \sqrt{d_F(v_i)^2+d_F(v_j)^2} $, where $ d_F(v_i) $ is the degree of the vertex $ v_i $ in graph $ F $. Also, the reduced Sombor index and the Average Sombor index have been introduced recently, and these topological indices have good predictive potential in mathematical chemistry. In this paper, we determine the extreme molecular graphs with the maximum value of Sombor index and the extremal connected graphs with the maximum (reduced) Sombor index. Some inequalities relations among the chemistry

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9

Kim, Hyoung Seok, Hong Oh Kim, and Sung Yong Shin. "Collision detection algorithm of a continuous type using spherical extreme vertex diagrams." Computers & Mathematics with Applications 47, no. 8-9 (2004): 1363–78. http://dx.doi.org/10.1016/s0898-1221(04)90129-0.

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10

Asmat, Farwa, Humaira Asmat, Sameh Askar, Hijaz Ahmad, and Muhammad Ijaz Khan. "On Weighted Vertex and Edge Mostar Index for Trees and Cacti with Fixed Parameter." European Journal of Pure and Applied Mathematics 16, no. 3 (2023): 1794–808. http://dx.doi.org/10.29020/nybg.ejpam.v16i3.4722.

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It was introduced by Doˇsli ́c and Ivica et al. (Journal of Mathematical chemistry, 56(10) (2018): 2995–3013), as an innovative graph-theoretic topological identifier, the Mostar index is significant in simulating compounds’ thermodynamic properties in simulations, which is defined as sum of absolute values of the differences among nu(e|Ω) and nv(e|Ω) over all lines e = uv ∈ Ω, where nu(e|Ω) (resp. nv(e|Ω)) is the collection of vertices of Ω closer to vertex u (resp. v) than to vertex v (resp. u). Let C(n, k) be the set of all n-vertex cacti graphs with exactly k cycles and T(n, d) be the set

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Estrada-Moreno, Alejandro, Erick Rodríguez-Bazan, and Juan Rodríguez-Velázquez. "On distances in generalized Sierpiński graphs." Applicable Analysis and Discrete Mathematics 12, no. 1 (2018): 49–69. http://dx.doi.org/10.2298/aadm160802001e.

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In this paper we propose formulas for the distance between vertices of a generalized Sierpi?ski graph S(G, t) in terms of the distance between vertices of the base graph G. In particular, we deduce a recursive formula for the distance between an arbitrary vertex and an extreme vertex of S(G, t), and we obtain a recursive formula for the distance between two arbitrary vertices of S(G, t) when the base graph is triangle-free. From these recursive formulas, we provide algorithms to compute the distance between vertices of S(G, t). In addition, we give an explicit formula for the diameter and radi

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12

Bisztriczky, Tibor. "An n-Vertex Theorem for Convex Space Curves." Canadian Journal of Mathematics 37, no. 2 (1985): 217–37. http://dx.doi.org/10.4153/cjm-1985-014-7.

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The classical four-vertex theorem states that a simple closed convex C2 curve in the Euclidean plane has at least four vertices (points of extreme curvature). This theorem has many generalizations with regard to both the curve and the topological space and for a history of the subject, we refer to [4] and [1]. The particular generalization of concern, credited to H. Mohrmann, is the following n-vertex theorem.Let a simple closed C3 curve on a closed convex surface be intersected by a suitable plane in n points. Then the curve has at least n inflections (vertices).The closed convex surface in t

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13

Ibe Iro, Uzoma, George Uwadiegwu Alaneme, Abdalrhman Milad, et al. "Optimization and Simulation of Saw Dust Ash Concrete Using Extreme Vertex Design Method." Advances in Materials Science and Engineering 2022 (September 24, 2022): 1–22. http://dx.doi.org/10.1155/2022/5082139.

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In this research study, a constrained simplex optimization method was adapted for the evaluation of green concrete’s mechanical property constituting of two-component mixture problem of cement and saw dust ash (SDA), which is a derivative from industrial residue. This experiential research will provide avenue for the recycle and incorporation of waste materials to achieve sustainability and control indiscriminate disposal of waste. The formulated components constrained were realized from the relevant literature studies to obtain the feasible planes in the simplex, and from this computation app

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De Ita, Guillermo, Pedro Bello López, and Meliza Contreras González. "Extreme Topologies on Bipolygonal Graphs and Dinamic Trees." International Journal of Combinatorial Optimization Problems and Informatics 14, no. 1 (2023): 19–26. https://doi.org/10.61467/2007.1558.2023.v14i1.335.

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We show how properties of the sequence βi,j, which represents the product between two Fibonacci's numbers Fi × Fj, can be used for the computation of the Merrifield-Simmons index on bipolygonal graphs and trees. We show that the extreme values of the Merrifield-Simmons index on bipolygonal graphs are found in two consecutive columns of the table βi,j k=i+j=1,...,n. The minimum value in β3,k-3 and the maximum value in β4,k-4. On the other hand we show that i(Tn ∪ {{vp, v}}) is minimum when v is a new leaf node, and its father vp was also a leaf node in Tn. Our methods does not require the expli

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15

Li, Chao, Chang Hong Liu, Xin Chuan Qin, and Yong Tai Li. "Fuzzy Finite Element Applications in the Waste Heat Boiler." Applied Mechanics and Materials 215-216 (November 2012): 1180–85. http://dx.doi.org/10.4028/www.scientific.net/amm.215-216.1180.

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A practical approach for analyzing the waste heat boiler with fuzzy parameters is developed. The methodology involves integrated finite element modeling and fuzzy analysis. The uncertainties in the material, loading and structural properties are represented using convex normal fuzzy sets. Vertex solution methodology that is based on α-cut representation is used for the fuzzy analysis. The values of the extreme responses at an α-level are obtained by applying the binary combinations of the fuzzy variables that result in extreme responses to the finite element model. The merit of the proposed me

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Frajna, Eszter, and Róbert Vértesi. "Correlation of Heavy and Light Flavors in Simulations." Universe 5, no. 5 (2019): 118. http://dx.doi.org/10.3390/universe5050118.

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The ALICE experiment at the Large Hadron Collider (LHC) ring is designed to study the strongly interacting matter at extreme energy densities created in high-energy heavy-ion collisions. In this paper we investigate correlations of heavy and light flavors in simulations at LHC energies at mid-rapidity, with the primary purpose of proposing experimental applications of these methods. Our studies have shown that investigating the correlation images can aid the experimental separation of heavy quarks and help understanding the physics that create them. The shape of the correlation peaks can be us

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Egorova, Evgeniya, Aleksey Mokryakov, and Vladimir Tsurkov. "The Algebra of Signatures for Extreme Two-Uniform Hypergraphs." Axioms 12, no. 12 (2023): 1123. http://dx.doi.org/10.3390/axioms12121123.

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In the last decade, several characterizations have been constructed for constructions such as extreme hypergraphs. One of the most recently described features is the signature. A signature is a number that uniquely describes an extremal and allows one to efficiently store the extremal two-uniform hypergraph itself. However, for the signature, although various algorithms have been derived for transforming it into other object-characteristics such as the base, the adjacency matrix, and the vector of vertex degrees, no isolated signature union and intersection apparatus has been constructed. This

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18

Shao, Zehui, Pu Wu, Huiqin Jiang, S. M. Sheikholeslami, and Shaohui Wang. "On the maximum ABC index of bipartite graphs without pendent vertices." Open Chemistry 18, no. 1 (2020): 39–49. http://dx.doi.org/10.1515/chem-2020-0002.

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AbstractFor a simple graph G, the atom–bond connectivity index (ABC) of G is defined as ABC(G) = $\sum_{uv\in{}E(G)} \sqrt{\frac{d(u)+d(v)-2}{d(u)d(v)}},$where d(v) denotes the degree of vertex v of G. In this paper, we prove that for any bipartite graph G of order n ≥ 6, size 2n − 3 with δ(G) ≥ 2, $ABC(G)\leq{}\sqrt{2}(n-6)+2\sqrt{\frac{3(n-2)}{n-3}}+2,$and we characterize all extreme bipartite graphs.

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19

GONNELLA, GIUSEPPE, and SEBASTIANO STRAMAGLIA. "PHASE DIAGRAM OF THE GAUGE INVARIANT TWO SPECIES ISING MODEL." Modern Physics Letters B 10, no. 01n02 (1996): 31–39. http://dx.doi.org/10.1142/s0217984996000067.

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We study the phase diagram of a Z(2) Higgs-gauge model with two species of Ising matter in D=2 and D=3. Differently from the case with only one Ising species, this model exhibits a transition also at zero gauge coupling. Loop expansions and mappings on the 8-vertex and the Ashkin–Teller models are used to study the nature of the transitions in the extreme regions of the phase diagram. Relevant differences with respect to the case of one species of Ising spins are found.

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20

Ma, Fei, Xudong Luo, and Ping Wang. "Stochastic growth tree networks with an identical fractal dimension: Construction and mean hitting time for random walks." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 6 (2022): 063123. http://dx.doi.org/10.1063/5.0093795.

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There is little attention paid to stochastic tree networks in comparison with the corresponding deterministic analogs in the current study of fractal trees. In this paper, we propose a principled framework for producing a family of stochastic growth tree networks [Formula: see text] possessing fractal characteristic, where [Formula: see text] represents the time step and parameter [Formula: see text] is the number of vertices newly created for each existing vertex at generation. To this end, we introduce two types of generative ways, i.e., Edge-Operation and Edge-Vertex-Operation. More interes

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21

Dogan, Derya, and Pinar Dundar. "The Average Covering Number of a Graph." Journal of Applied Mathematics 2013 (2013): 1–4. http://dx.doi.org/10.1155/2013/849817.

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There are occasions when an average value of a graph parameter gives more useful information than the basic global value. In this paper, we introduce the concept of the average covering number of a graph (the covering number of a graph is the minimum number of vertices in a set with the property that every edge has a vertex in the set). We establish relationships between the average covering number and some other graph parameters, find the extreme values of the average covering number among all graphs of a given order, and find the average covering number for some families of graphs.

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22

Knor, Martin, Muhammad Imran, Muhammad Kamran Jamil та Riste Škrekovski. "Remarks on Distance Based Topological Indices for ℓ-Apex Trees". Symmetry 12, № 5 (2020): 802. http://dx.doi.org/10.3390/sym12050802.

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A graph G is called an ℓ-apex tree if there exist a vertex subset A ⊂ V ( G ) with cardinality ℓ such that G − A is a tree and there is no other subset of smaller cardinality with this property. In the paper, we investigate extremal values of several monotonic distance-based topological indices for this class of graphs, namely generalized Wiener index, and consequently for the Wiener index and the Harary index, and also for some newer indices as connective eccentricity index, generalized degree distance, and others. For the one extreme value we obtain that the extremal graph is a join of a tre

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Chen, Guojun, and Rongji Wang. "Triangular Mesh Surface Subdivision Based on Graph Neural Network." Applied Sciences 14, no. 23 (2024): 11378. https://doi.org/10.3390/app142311378.

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Mesh subdivision is a common mesh-processing algorithm used to improve model accuracy and surface smoothness. Its classical scheme adopts a fixed linear vertex update strategy and is implemented iteratively, which often results in excessive mesh smoothness. In recent years, a nonlinear subdivision method that uses neural network methods, called neural subdivision (NS), has been proposed. However, as a new scheme, its application scope and the effect of its algorithm need to be improved. To solve the above problems, a graph neural network method based on neural subdivision was used to realize m

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Vinoth, J., and J. Bruce Ralphin Rose. "Dynamic stability characterization of re-entry modules at hypersonic mach numbers." International Journal of Modeling, Simulation, and Scientific Computing 08, no. 01 (2017): 1750010. http://dx.doi.org/10.1142/s1793962317500106.

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At the time of re-entry modules entering into the atmosphere from space, a small perturbation introduces dynamic oscillations on the vehicle because of their extreme traveling speed. The dynamic stability characteristics of re-entry modules at hypersonic Mach numbers is of considerable relevance to their initial design. In the present paper, the dynamic stability of blunt cone model about [Formula: see text] is examined with wide range of design parameters such as nose bluntness, semi-vertex angle and center of rotation through theoretical and experimental methods. Theoretical approximations a

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Wang, Liangkai, Yalu Shao, Zilong Zhao, Shuang Chen, and Xiaohou Shao. "Optimized utilization studies of dredging sediment for making water treatment ceramsite based on an extreme vertex design." Journal of Water Process Engineering 38 (December 2020): 101603. http://dx.doi.org/10.1016/j.jwpe.2020.101603.

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Traverso, Simone, Niccolò Traverso Ziani, and Maura Sassetti. "Effects of the Vertices on the Topological Bound States in a Quasicrystalline Topological Insulator." Symmetry 14, no. 8 (2022): 1736. http://dx.doi.org/10.3390/sym14081736.

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The experimental realization of twisted bilayer graphene strongly pushed the inspection of bilayer systems. In this context, it was recently shown that a two layer Haldane model with a thirty degree rotation angle between the layers represents a higher order topological insulator, with zero-dimensional states isolated in energy and localized at the physical vertices of the nanostructure. We show, within a numerical tight binding approach, that the energy of the zero dimensional states strongly depends on the geometrical structure of the vertices. In the most extreme cases, once a specific band

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SIROTKIN, R. O., O. S. SIROTKIN, and A. M. PAVLOVA. "ON THE ‘DEGENERATION’ OF CHEMICAL BONDS WITHIN A UNIFIED MODEL AND SYSTEM COMBINING BASIC CLASSES OF CHEMICAL SUBSTANCES." Herald of Technological University 28, no. 5 (2025): 129–34. https://doi.org/10.55421/3034-4689_2025_28_5_129.

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Based on a unified model of chemical bonding that combines its three extreme types (covalent, metallic, and ionic) in the form of mixed homo- and heteronuclear classes, for the first time within the system of chemical bonds and compounds (SCBC) in the form of a ‘chemical triangle,’ the boundary of their ‘degeneration’ has been determined, beyond which they cease to exist. Within this model, the ‘degeneration’ of a chemical bond occurs through the gradual transformation of an extremely covalent localised chemical bond into bonds mixed with its metallic or ionic varieties. As a result, there is

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Gispert-Fernández, Adrià, and Juan Alberto Rodríguez-Velázquez. "The equidistant dimension of graphs: NP-completeness and the case of lexicographic product graphs." AIMS Mathematics 9, no. 6 (2024): 15325–45. http://dx.doi.org/10.3934/math.2024744.

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<abstract><p>Let $ V(G) $ be the vertex set of a simple and connected graph $ G $. A subset $ S\subseteq V(G) $ is a distance-equalizer set of $ G $ if, for every pair of vertices $ u, v\in V(G)\setminus S $, there exists a vertex in $ S $ that is equidistant to $ u $ and $ v $. The minimum cardinality among the distance-equalizer sets of $ G $ is the equidistant dimension of $ G $, denoted by $ \xi(G) $. In this paper, we studied the problem of finding $ \xi(G\circ H) $, where $ G\circ H $ denotes the lexicographic product of two graphs $ G $ and $ H $. The aim was to express $ \x

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Kuburovic, Vladimir, Vladislav Vukomanovic, Jovan Kosutic, et al. "Adams-Oliver syndrome: Case report." Srpski arhiv za celokupno lekarstvo 139, no. 3-4 (2011): 221–24. http://dx.doi.org/10.2298/sarh1104221k.

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Introduction. Adams-Oliver syndrome is characterized by congenital aplasia of the vertex skin of the skull in combination with skull and transverse limb defects. Case Outline. We presented a 5-month old female infant with Adams-Oliver syndrome manifested as cutis marmorata, dilated scalp veins and limb reduction defects. Clinical manifestation also included thumb hypoplasia and extreme hypoplasia of other fingers, with agenesis of all toes on both feet. Echocardiogram revealed foramen ovale apertum. Venography showed dilated malformed scalp and neck veins, predominantly on the right side. On t

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Uspenskii, A. A., and P. D. Lebedev. "On the structure of the singular set of solutions in one class of 3D time-optimal control problems." Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki 31, no. 3 (2021): 471–86. http://dx.doi.org/10.35634/vm210309.

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A class of time-optimal control problems in terms of speed in three-dimensional space with a spherical velocity vector is considered. A smooth regular curve $\Gamma$ was chosen as the target set. Pseudo-vertices — characteristic points on $\Gamma,$ responsible for the appearance of a singularity in the optimal result function, are selected. The characteristic features of the structure of a singular set belonging to the family of bisectors are revealed. An analytical representation is found for the extreme points of the bisector corresponding to a fixed pseudo-vertex. As an illustration of the

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Spinosa, Mônica Jaques, and Eliana Garzon. "Sleep spindles: validated concepts and breakthroughs." Journal of Epilepsy and Clinical Neurophysiology 13, no. 4 (2007): 179–82. http://dx.doi.org/10.1590/s1676-26492007000400006.

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INTRODUCTION: Sleep spindles, the hallmark of sleep synchronization in stage 2 non-REM sleep, are rhythmic and monomorphic waves, between 10 and 14 Hz, with a maximum amplitude in the vertex (Cz), with bilateral irradiation to central regions (C3 and C4). OBJECTIVE: In this article we present an overview of sleep spindles ranging from well established concepts of morphology, generation mechanisms, maturational features, abnormal patterns and pathological aspects since the knowledge is important to identify the normal and abnormal patterns. CONCLUSION: Centro-parietal and frontal spindle are no

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Lebedev, Pavel D., and Alexander A. Uspenskii. "Elements of analytical solutions constructor in a class of time-optimal control problems with the break of curvature of a target set." Russian Universities Reports. Mathematics, no. 132 (2020): 370–86. http://dx.doi.org/10.20310/2686-9667-2020-25-132-370-386.

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A planar velocity control problem with a disc indicatrix and a target set with a smooth boundary having finite discontinuities of second-order derivatives of coordinate functions is considered. We have studied pseudo-vertices-special points of the goal boundary that generate a singularity for the optimal control function. For non-stationary pseudo-vertices with discontinuous curvature, one-way markers are found, the values of which are necessary for analytical and numerical construction of branches of a singular set. It is proved that the markers lie on the border of the spectrum-the region of

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Das, Kinkar Chandra, and Jayanta Bera. "Resolving an Open Problem on the Exponential Arithmetic–Geometric Index of Unicyclic Graphs." Mathematics 13, no. 9 (2025): 1391. https://doi.org/10.3390/math13091391.

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Recently, the exponential arithmetic–geometric index (EAG) was introduced. The exponential arithmetic–geometric index (EAG) of a graph G is defined as EAG(G)=∑vivj∈E(G)edi+dj2didj, where di represents the degree of the vertex vi in G. The characterization of extreme structures in relation to graph invariants from the class of unicyclic graphs is an important problem in discrete mathematics. Cruz et al., 2022 proposed a unified method for finding extremal unicyclic graphs for exponential degree-based graph invariants. However, in the case of EAG, this method is insufficient for generating the m

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Liu, Jinhui, and Qiangqiang Xu. "Characteristics and method of curing of phosphogypsum road stabilizing materials enhanced with sodium silicate." Mari Papel y Corrugado 2025 (May 17, 2025): 95–104. https://doi.org/10.71442/mari2025-0011.

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Because of its vast deposits and slow rate of resource utilization, phosphogypsum (PG), a by-product of the production of phosphate fertilizer, has emerged as a pressing environmental issue. In this study, sodium silicate was blended into PG road stabilizers to change their properties, and the curing method was examined. The ideal mixture was identified by optimizing the ratios of PG, cement (C), silica fume (SF), and slaked lime (SL) using the extreme vertex mixing scheme. Based on this, various ratios of sodium silicate were externally doped, and the changed materials’ strength characteristi

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Anwar, Shabana, Muhammad Kamran Jamil, Amal S. Alali, Mehwish Zegham, and Aisha Javed. "Extremal values of the first reformulated Zagreb index for molecular trees with application to octane isomers." AIMS Mathematics 9, no. 1 (2024): 289–301. http://dx.doi.org/10.3934/math.2024017.

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<abstract><p>A connected acyclic graph in which the degree of every vertex is at most four is called a molecular tree. A number associated with a molecular tree that can help to approximate the physical or chemical properties of the corresponding molecule is called a topological index. It is of great importance to investigate the relation between the structure and the thermodynamic properties of those molecules. In this paper, we investigated the extreme value of the first reformulated Zagreb index with a given order and degree of a graph. Further, we investigated the molecular tre

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Gillman, Andrew, Gregory Wilson, Kazuko Fuchi, Darren Hartl, Alexander Pankonien, and Philip Buskohl. "Design of Soft Origami Mechanisms with Targeted Symmetries." Actuators 8, no. 1 (2018): 3. http://dx.doi.org/10.3390/act8010003.

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The integration of soft actuating materials within origami-based mechanisms is a novel method to amplify the actuated motion and tune the compliance of systems for low stiffness applications. Origami structures provide natural flexibility given the extreme geometric difference between thickness and length, and the energetically preferred bending deformation mode can naturally be used as a form of actuation. However, origami fold patterns that are designed for specific actuation motions and mechanical loading scenarios are needed to expand the library of fold-based actuation strategies. In this

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Biswas, EH, MA Islam, R. Ferdowsi, YA Yusof, and MG Aziz. "Effect of sugar and starch on chemical and organoleptic parameters of pineapple bar during storage." Progressive Agriculture 30, no. 2 (2019): 227–37. http://dx.doi.org/10.3329/pa.v30i2.42519.

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The aim of this study was to assess the effect of major ingredients on the changes of fundamental quality parameters of pineapple fruit bar during preparation and storage. Four samples were prepared by using Extreme Vertex mixture taking three major ingredients namely fruit pulp, sugar and starch content as factors and non-enzymatic browning data and overall acceptability as responses. The result revealed that compositional differences of different ingredients in formulation fitted to the quadratic linear model at p<0.05. Among the four formulations the liking intensity of formulation F4 co

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Rao, Pooja, Michael Francis McCullough, Jessica Stevens, and Matthew A. Edwardson. "Grief-induced reversible cerebral vasoconstriction syndrome (RCVS)." BMJ Case Reports 13, no. 1 (2020): e232204. http://dx.doi.org/10.1136/bcr-2019-232204.

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Stress is under-recognised as a potential causative factor for reversible cerebral vasoconstriction syndrome (RCVS). Here we present a case of RCVS occurring during a time of extreme emotional duress. A 46-year-old female patient with medical history of bipolar disorder developed a severe headache during her father’s funeral. The following day she was discovered to have bilateral hemiparesis, aphasia, encephalopathy and was brought emergently to the hospital. Neuroimaging revealed a 33 mL left fronto-parietal haematoma with subarachnoid blood near the vertex bilaterally. She underwent cranioto

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Hassan, Javier, and Sergio Canoy, Jr. "Grundy Hop Domination in Graphs." European Journal of Pure and Applied Mathematics 15, no. 4 (2022): 1623–36. http://dx.doi.org/10.29020/nybg.ejpam.v15i4.4511.

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Let G be an undirected graph with vertex and edge sets V (G) and E(G), respectively. Let S = (v1, v2, · · · , vk) be a sequence of distinct vertices of G and let Sˆ = {v1, v2, . . . , vk}. Then S is a legal closed hop neighborhood sequence of G if N2 G[vi]\∪i−1j=1N 2 G[vj ] ̸= ∅ for each i ∈ {2, · · · , k}. If, in addition, Sˆ is a hop dominating set of G, then S is called a Grundy hop dominating sequence.The maximum length of a Grundy hop dominating sequence in a graph G, denoted by γ hgr(G), is called the Grundy hop domination number of G. In this paper, we determine some (extreme) values fo

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Pérez Lara, Carlos E. "The sPHENIX Experiment." EPJ Web of Conferences 171 (2018): 10002. http://dx.doi.org/10.1051/epjconf/201817110002.

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Our understanding of QCD under extreme conditions has advanced tremendously in the last 20 years with the discovery of the Quark Gluon Plasma and its characterisation in heavy ion collisions at RHIC and LHC. The sPHENIX detector planned at RHIC is designed to further study the microscopic nature of the QGP through precision measurements of jet, upsilon and open heavy flavor probes over a broad pT range. The multi-year sPHENIX physics program will commence in early 2023, using state-of-the art detector technologies to fully exploit the highest RHIC luminosities. The experiment incorporates the

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Koam, Ali N. A., Muhammad Faisal Nadeem, Ali Ahmad, and Hassan A. Eshaq. "Weighted Asymmetry Index: A New Graph-Theoretic Measure for Network Analysis and Optimization." Mathematics 12, no. 21 (2024): 3397. http://dx.doi.org/10.3390/math12213397.

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Graph theory is a crucial branch of mathematics in fields like network analysis, molecular chemistry, and computer science, where it models complex relationships and structures. Many indices are used to capture the specific nuances in these structures. In this paper, we propose a new index, the weighted asymmetry index, a graph-theoretic metric quantifying the asymmetry in a network using the distances of the vertices connected by an edge. This index measures how uneven the distances from each vertex to the rest of the graph are when considering the contribution of each edge. We show how the i

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Cabrera Martinez, Abel. "Starred Italian domination in graphs." Contributions to Discrete Mathematics 16, no. 3 (2021): 139–52. http://dx.doi.org/10.55016/ojs/cdm.v16i3.71109.

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An Italian dominating function on a graph $G$ is a function $f:V(G)\rightarrow \{0,1,2\}$ such that $\sum_{u\in N(v)}f(u)\geq 2$ for every vertex $v\in V_0$, where $V_0=\{v\in V(G) : f(v)=0\}$ and $N(v)$ represents the open neighbourhood of $v$. A starred Italian dominating function on $G$ is an Italian dominating function $f$ such that $V_0$ is not a dominating set of $G$. The starred Italian domination number of $G$, denoted $\gamma_{I}^*(G)$, is the minimum weight $\omega(f)=\sum_{v\in V(G)}f(v)$ among all starred Italian dominating functions $f$ on $G$. In this article, we initiate the stu

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Maiyer, Fedor F., Meyrambek G. Tastanov, and Anar A. Utemissova. "On a subclass of close-to-convex functions related to starlike functions of order 1/2." Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, no. 94 (2025): 5–23. https://doi.org/10.17223/19988621/94/1.

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The article introduces and investigates a special subclass of close-to-convex functions in a unit disk which is defined in terms of starlike functions of the order 1/2. Functions of this class, as well as starlike functions of the order 1/2, may have omissions in the decomposition. Some close subclasses have been actively studied in the works of Gao C.-Y., Zhou S.-Q., Kowalczyk J., Les-Bomba E., Prajapat J.K., and other authors published in the last decade. The class of functions introduced in this paper is characterized by the fact that the range of values of the functional used is contained

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de Brito, J. B., C. I. N. Sampaio Filho, A. A. Moreira, and J. S. Andrade. "Characterizing the intrinsic correlations of scale-free networks." International Journal of Modern Physics C 27, no. 03 (2016): 1650024. http://dx.doi.org/10.1142/s0129183116500248.

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When studying topological or dynamical properties of random scale-free networks, it is tacitly assumed that degree–degree correlations are not present. However, simple constraints, such as the absence of multiple edges and self-loops, can give rise to intrinsic correlations in these structures. In the same way that Fermionic correlations in thermodynamic systems are relevant only in the limit of low temperature, the intrinsic correlations in scale-free networks are relevant only when the extreme values for the degrees grow faster than the square root of the network size. In this situation, the

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Lotfi, Abdullah, Abbe Mowshowitz, and Matthias Dehmer. "A Note on Eigenvalues and Asymmetric Graphs." Axioms 12, no. 6 (2023): 510. http://dx.doi.org/10.3390/axioms12060510.

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This note is intended as a contribution to the study of quantitative measures of graph complexity that use entropy measures based on symmetry. Determining orbit sizes of graph automorphism groups is a key part of such studies. Here we focus on an extreme case where every orbit contains just a single vertex. A permutation of the vertices of a graph G is an automorphism if, and only if, the corresponding permutation matrix commutes with the adjacency matrix of G. This fact establishes a direct connection between the adjacency matrix and the automorphism group. In particular, it is known that if

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Ibarra-Rondón, Aldo, Dinary Eloisa Durán-Sequeda, Andrea Carolina Castro-Pacheco, Pedro Fragoso-Castilla, Rolando Barahona-Rosales, and José Edwin Mojica-Rodríguez. "Optimization of Palm Kernel Cake Bioconversion with P. ostreatus: An Efficient Lignocellulosic Biomass Value-Adding Process for Ruminant Feed." Fermentation 11, no. 5 (2025): 251. https://doi.org/10.3390/fermentation11050251.

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This study aims to optimize the bioconversion of palm kernel cake (PKC) by Pleurotus ostreatus to improve fungal biomass production, lignocellulolytic enzyme expression, and the nutritional value of the substrate as ruminant feed. Three inorganic nitrogen sources (ammonium sulfate, ammonium nitrate, and urea) were evaluated for fungal biomass production using a central composite design (CCD) in liquid fermentations. The formulated culture medium (18.72 g/L glucose and 0.39 g/L urea) effectively yielded better fungal biomass production (8 g/L). Based on these results, an extreme vertex design,

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Aviles-Rivera, Yudit Aimee, José Benigno Valdez-Torres, Juan Pedro Campos-Sauceda, José Basilio Heredia, Jeny Hinojosa-Gómez, and María Dolores Muy-Rangel. "Designing of an Oat-Mango Molded Snack with Feasible Nutritional and Nutraceutical Properties." Foods 13, no. 21 (2024): 3402. http://dx.doi.org/10.3390/foods13213402.

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In recent years, the market has seen a growing demand for healthy and convenient food options, such as fruit and cereal bars, driven by shifts in eating habits. These changes are primarily attributed to time constraints in meal preparation and the need for ready-to-eat foods. Consequently, this has promoted interest in creating a nutritious, high-quality snack combining oats and mango. This study employed a response surface analysis of extreme vertex mixtures, incorporating constraints and three components: oats, mango peel, and dehydrated mango pulp. This resulted in ten different mixtures, e

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Sclosa, Davide. "Completely degenerate equilibria of the Kuramoto model on networks." Nonlinearity 37, no. 9 (2024): 095021. http://dx.doi.org/10.1088/1361-6544/ad694a.

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Abstract Kuramoto Networks contain non-hyperbolic equilibria whose stability is sometimes difficult to determine. We consider the extreme case in which all Jacobian eigenvalues are zero. In this case linearizing the system at the equilibrium leads to a Jacobian matrix which is zero in every entry. We call these equilibria completely degenerate. We prove that they exist for certain intrinsic frequencies if and only if the underlying graph is bipartite, and that they do not exist for generic intrinsic frequencies. In the case of zero intrinsic frequencies, we prove that they exist if and only if

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Onyelowe, Kennedy C., George Alaneme, Duc Bui Van, et al. "Generalized Review on EVD and Constraints Simplex Method of Materials Properties Optimization for Civil Engineering." Civil Engineering Journal 5, no. 3 (2019): 729. http://dx.doi.org/10.28991/cej-2019-03091283.

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Extreme vertex design (EVD) has been adapted to be used in the modeling of the behavior of mixture experiments in civil engineering. This method has been in use since the 1970s and has be prevalent in the field of medical science. Various other methods of design of experiments have been used in engineering but neither has EVD being used particularly in civil engineering. This review is presented to serve as a hub or guide for subsequent exercise where concrete production, asphalt production or modification, soils stabilization and concrete improvement or water treatment would be studied with t

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Lopuhaä-Zwakenberg, Milan, and Jasper Goseling. "Mechanisms for Robust Local Differential Privacy." Entropy 26, no. 3 (2024): 233. http://dx.doi.org/10.3390/e26030233.

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We consider privacy mechanisms for releasing data X=(S,U), where S is sensitive and U is non-sensitive. We introduce the robust local differential privacy (RLDP) framework, which provides strong privacy guarantees, while preserving utility. This is achieved by providing robust privacy: our mechanisms do not only provide privacy with respect to a publicly available estimate of the unknown true distribution, but also with respect to similar distributions. Such robustness mitigates the potential privacy leaks that might arise from the difference between the true distribution and the estimated one

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