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Journal articles on the topic 'Adjacency energy'

Author: Grafiati

Published: 7 June 2025

Last updated: 2 August 2025

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1

Paulin, S. Shiny, and T. Bharathi. "Adjacency Sequence and Adjacency Spectrum of Power Fuzzy Graphs." Indian Journal Of Science And Technology 17, no. 47 (2024): 5016–24. https://doi.org/10.17485/ijst/v17i47.3605.

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Objectives: To find the adjacency sequence, spectrum of the power fuzzy graphs and discuss its properties. Methods: The spectrum and energy of the power fuzzy graphs are derived using the adjacency matrices. Energy of the power fuzzy graph is computed by adding the absolute eigenvalues of the adjacency matrix. Findings: The condition for a power fuzzy graph, 𝐺𝑓 𝑘 to be vertex regular in terms of adjacency sequence has been verified. The energy sequence for the power fuzzy graph with increasing 𝑘 has been established. Novelty: The concept of minimizing the interval of the edge membership values

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2

Shanmugavel, Vimala, and Sakunthala Srinivasan. "Investigation on Pebbling Energy for Standard Graphs." Indian Journal Of Science And Technology 17, no. 32 (2024): 3327–34. http://dx.doi.org/10.17485/ijst/v17i32.1962.

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Objectives: Introducing the idea of energy pebbling to path, star, tree, and cycle graphs is the main objective of this study. The sum of the absolute values of the eigenvalues in the adjacency matrix of a pebbling network is its energy. We then construct the upper and lower bounds for the aforementioned graphs in this discussion. Methods: Removing two pebbles from the first vertex and placing one pebble on the neighboring vertex illustrates a pebbling move. The pebbling graph's adjacency matrix is computed as where is the edge value of is adjacent to . The energy of the graph is calculated us

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3

S, Shiny Paulin, and Bharathi T. "Adjacency Sequence and Adjacency Spectrum of Power Fuzzy Graphs." Indian Journal of Science and Technology 17, no. 47 (2024): 5016–24. https://doi.org/10.17485/IJST/v17i47.3605.

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Abstract <strong>Objectives:</strong> To find the adjacency sequence, spectrum of the power fuzzy graphs and discuss its properties.<strong> Methods:</strong> The spectrum and energy of the power fuzzy graphs are derived using the adjacency matrices. Energy of the power fuzzy graph is computed by adding the absolute eigenvalues of the adjacency matrix. <strong>Findings:</strong> The condition for a power fuzzy graph, 𝐺𝑓 𝑘 to be vertex regular in terms of adjacency sequence has been verified. The energy sequence for the power fuzzy graph with increasing 𝑘 has been estab

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4

Keerthi G. Mirajkar and Anuradha V. Deshpande. "Some Properties of Block Adjacency Energy." Journal of Computational Mathematica 7, no. 1 (2023): 006–16. http://dx.doi.org/10.26524/cm158.

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Block adjacency energy EBA(G) is the sum of eigenvalues of block adjacency matrix BA(G). The present research work intends to study some properties of block adjacency energy such as block adjacency equienergetic, hyperenergetic, nonhyperenergetic, borderenergetic, hypoenergetic and blockenergetic graphs using block adjacency matrix. It is also verified the existence of smith graph.

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Srinivasan, Sakunthala, and Vimala Shanmugavel. "Adjacency energy of pebbling graphs." Journal of Physics: Conference Series 1850, no. 1 (2021): 012089. http://dx.doi.org/10.1088/1742-6596/1850/1/012089.

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6

Romdhini, Mamika Ujianita, and Athirah Nawawi. "On the Spectral Radius and Sombor Energy of the Non-Commuting Graph for Dihedral Groups." Malaysian Journal of Fundamental and Applied Sciences 20, no. 1 (2024): 65–73. http://dx.doi.org/10.11113/mjfas.v20n1.3252.

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The non-commuting graph, denoted by , is defined on a finite group , with its vertices are elements of excluding those in the center of . In this graph, two distinct vertices are adjacent whenever they do not commute in . The graph can be associated with several matrices including the most basic matrix, which is the adjacency matrix, , and a matrix called Sombor matrix, denoted by . The entries of are either the square root of the sum of the squares of degrees of two distinct adjacent vertices, or zero otherwise. Consequently, the adjacency and Sombor energies of is the sum of the absolute eig

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7

Kurian, Liya Jess, and Chithra Velu. "Bounds for the Energy of Hypergraphs." Axioms 13, no. 11 (2024): 804. http://dx.doi.org/10.3390/axioms13110804.

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The concept of the energy of a graph has been widely explored in the field of mathematical chemistry and is defined as the sum of the absolute values of the eigenvalues of its adjacency matrix. The energy of a hypergraph is the trace norm of its connectivity matrices, which generalize the concept of graph energy. In this paper, we establish bounds for the adjacency energy of hypergraphs in terms of the number of vertices, maximum degree, eigenvalues, and the norm of the adjacency matrix. Additionally, we compute the sum of squares of adjacency eigenvalues of linear k-hypergraphs and derive its

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8

Altassan, Alaa, Hilal A. Ganie, and Yilun Shang. "On the Extended Adjacency Eigenvalues of a Graph." Information 15, no. 10 (2024): 586. http://dx.doi.org/10.3390/info15100586.

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Let H be a graph of order n with m edges. Let di=d(vi) be the degree of the vertex vi. The extended adjacency matrix Aex(H) of H is an n×n matrix defined as Aex(H)=(bij), where bij=12didj+djdi, whenever vi and vj are adjacent and equal to zero otherwise. The largest eigenvalue of Aex(H) is called the extended adjacency spectral radius of H and the sum of the absolute values of its eigenvalues is called the extended adjacency energy of H. In this paper, we obtain some sharp upper and lower bounds for the extended adjacency spectral radius in terms of different graph parameters and characterize

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9

Vimala, Shanmugavel, and Srinivasan Sakunthala. "Investigation on Pebbling Energy for Standard Graphs." Indian Journal of Science and Technology 17, no. 32 (2024): 3327–34. https://doi.org/10.17485/IJST/v17i32.1962.

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Abstract <strong>Objectives:</strong> Introducing the idea of energy pebbling to path, star, tree, and cycle graphs is the main objective of this study. The sum of the absolute values of the eigenvalues in the adjacency matrix of a pebbling network is its energy. We then construct the upper and lower bounds for the aforementioned graphs in this discussion. <strong>Methods:</strong> Removing two pebbles from the first vertex and placing one pebble on the neighboring vertex illustrates a pebbling move. The pebbling graph's adjacency matrix is computed as where is the edge value of

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10

Wang, Yajing, and Yubin Gao. "Nordhaus–Gaddum-Type Relations for Arithmetic-Geometric Spectral Radius and Energy." Mathematical Problems in Engineering 2020 (July 16, 2020): 1–7. http://dx.doi.org/10.1155/2020/5898735.

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Spectral graph theory plays an important role in engineering. Let G be a simple graph of order n with vertex set V=v1,v2,…,vn. For vi∈V, the degree of the vertex vi, denoted by di, is the number of the vertices adjacent to vi. The arithmetic-geometric adjacency matrix AagG of G is defined as the n×n matrix whose i,j entry is equal to di+dj/2didj if the vertices vi and vj are adjacent and 0 otherwise. The arithmetic-geometric spectral radius and arithmetic-geometric energy of G are the spectral radius and energy of its arithmetic-geometric adjacency matrix, respectively. In this paper, some new

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11

Kaladevi, V., and G. Kavitha. "Energy of chemical graphs with adjacency rhotrix." World Review of Science, Technology and Sustainable Development 1, no. 1 (2021): 1. http://dx.doi.org/10.1504/wrstsd.2021.10034899.

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12

Khan, Mehtab, Rashid Farooq, and Juan Rada. "Complex adjacency matrix and energy of digraphs." Linear and Multilinear Algebra 65, no. 11 (2016): 2170–86. http://dx.doi.org/10.1080/03081087.2016.1265064.

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13

Fernández, Ariel. "Homology of Potential Energy Surfaces." Zeitschrift für Naturforschung A 41, no. 9 (1986): 1118–22. http://dx.doi.org/10.1515/zna-1986-0905.

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It is shown that all the adjacency relations for the basins of attraction of stable chemical species and transition states can be derived from the topology of the pattern of intrinsic-reaction-coordinate- and-separatix trajectories in the nuclear configuration space.The results are applied to thermal [1,3] sigmatropic rearrangements and they show that even the symmetry-forbidden path proceeds concertedly. The corresponding homological formulas giving the adjacency relations are derived.

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14

OZ, Mert Sinan. "Coefficients of Randic and Sombor characteristic polynomials of some graph types." Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics 71, no. 3 (2022): 778–90. http://dx.doi.org/10.31801/cfsuasmas.1080426.

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Let GG be a graph. The energy of GG is defined as the summation of absolute values of the eigenvalues of the adjacency matrix of GG. It is possible to study several types of graph energy originating from defining various adjacency matrices defined by correspondingly different types of graph invariants. The first step is computing the characteristic polynomial of the defined adjacency matrix of GG for obtaining the corresponding energy of GG. In this paper, formulae for the coefficients of the characteristic polynomials of both the Randic and the Sombor adjacency matrices of path graph PnPn , c

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15

Yousefi, Najibullah, Amrullah Awsar, and Laila Popalzai. "Energy of Graph." Journal for Research in Applied Sciences and Biotechnology 2, no. 1 (2023): 13–17. http://dx.doi.org/10.55544/jrasb.2.1.3.

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By given the adjacency matrix, laplacian matrix of a graph we can find the set of eigenvalues of graph in order to discussed about the energy of graph and laplacian energy of graph. (i.e. the sum of eigenvalues of adjacency matrix and laplacian matrix of a graph is called the energy of graph) and the laplacian energy of graph is greater or equal to zero for any graph and is greater than zero for every connected graph with more or two vertices (i.e. the last eigenvalues of laplacian matrix is zero), according to several theorems about the energy of graph and the laplacian energy of graph that a

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16

GOK, GULISTAN KAYA, and SERIFE BUYUKK OSE. "SOME NOTES ON THE LAPLACIAN ENERGY OF EXTENDED ADJACENCY MATRIX." Journal of Science and Arts 20, no. 3 (2020): 511–18. http://dx.doi.org/10.46939/j.sci.arts-20.3-a01.

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The extended adjacency matrix Ae(G) of a graph G is determined by graph degrees. Some inequalities are found for the extended adjacency matrix including its vertices, its edges and its degrees in this paper. Also, some bounds are established for this matrix involving its energy and its Laplacian energy.

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17

Zhang, Haixia, та Zhuolin Zhang. "Some New Bounds for α-Adjacency Energy of Graphs". Mathematics 11, № 9 (2023): 2173. http://dx.doi.org/10.3390/math11092173.

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Let G be a graph with the adjacency matrix A(G), and let D(G) be the diagonal matrix of the degrees of G. Nikiforov first defined the matrix Aα(G) as Aα(G)=αD(G)+(1−α)A(G), 0≤α≤1, which shed new light on A(G) and Q(G)=D(G)+A(G), and yielded some surprises. The α−adjacency energy EAα(G) of G is a new invariant that is calculated from the eigenvalues of Aα(G). In this work, by combining matrix theory and the graph structure properties, we provide some upper and lower bounds for EAα(G) in terms of graph parameters (the order n, the edge size m, etc.) and characterize the corresponding extremal gr

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18

Ahmad, Zaheer, Zeeshan Saleem Mufti, Muhammad Faisal Nadeem, Hani Shaker, and Hafiz Muhammad Afzal Siddiqui. "Theoretical study of energy, inertia and nullity of phenylene and anthracene." Open Chemistry 19, no. 1 (2021): 541–47. http://dx.doi.org/10.1515/chem-2020-0160.

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Abstract Energy of a molecule plays an important role in physics, chemistry and biology. In mathematics, the concept of energy is used in graph theory to help other subjects such as chemistry and physics. In graph theory, nullity is the number of zeros extracted from the characteristic polynomials obtained from the adjacency matrix, and inertia represents the positive and negative eigenvalues of the adjacency matrix. Energy is the sum of the absolute eigenvalues of its adjacency matrix. In this study, the inertia, nullity and signature of the aforementioned structures have been discussed.

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19

Shanmukha, B., H. N. Shwetha та N. Manjunath. "Bounds for α—Adjacency Energy of a Graph". IOP Conference Series: Materials Science and Engineering 1070, № 1 (2021): 012019. http://dx.doi.org/10.1088/1757-899x/1070/1/012019.

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20

Andrews, David L., and Shaopeng Li. "Energy flow in dendrimers: An adjacency matrix representation." Chemical Physics Letters 433, no. 1-3 (2006): 239–43. http://dx.doi.org/10.1016/j.cplett.2006.11.049.

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21

Ramane, Harishchandra S., Hemaraddi N. Maraddi, and Raju B. Jummannaver. "Degree Subtraction Adjacency Eigenvalues and Energy of Graphs." Journal of Computer and Mathematical Sciences 9, no. 11 (2018): 1661–70. http://dx.doi.org/10.29055/jcms/908.

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22

Srinivasan, Sakunthala, and Vimala Shanmugavel. "Comparative Study on Different Types of Energies." Indian Journal Of Science And Technology 17, no. 28 (2024): 2954–59. http://dx.doi.org/10.17485/ijst/v17i28.1447.

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Objectives : The absolute sum of the eigenvalues is the definition of the graph's energy. In addition to discussing their relationship, this study compares the energy of the Adjacency matrix, Laplacian matrix, Signless Laplacian matrix, and Seidel matrix applied to ten distinct kinds of graphs. In this study, a correlation is established between the energy of graphs and the energy of Edge Antimagic graphs. Methods: The technical description of the graph's energy, . An Edge Antimagic graph's energy, identified by (G) = , is the absolute total of its eigenvalues. Findings: The energy was calcula

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23

Jog, S. R., and Raju Kotambari. "On the Adjacency, Laplacian, and Signless Laplacian Spectrum of Coalescence of Complete Graphs." Journal of Mathematics 2016 (2016): 1–11. http://dx.doi.org/10.1155/2016/5906801.

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Coalescence as one of the operations on a pair of graphs is significant due to its simple form of chromatic polynomial. The adjacency matrix, Laplacian matrix, and signless Laplacian matrix are common matrices usually considered for discussion under spectral graph theory. In this paper, we compute adjacency, Laplacian, and signless Laplacian energy (Qenergy) of coalescence of pair of complete graphs. Also, as an application, we obtain the adjacency energy of subdivision graph and line graph of coalescence from itsQenergy.

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24

Mufti, Zeeshan Saleem, Rukhshanda Anjum, Qin Xin, Fairouz Tchier, Iram Anwar-ul-Haq, and Yaé Ulrich Gaba. "Computing the Energy and Estrada Index of Different Molecular Structures." Journal of Chemistry 2022 (January 28, 2022): 1–7. http://dx.doi.org/10.1155/2022/6227093.

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Graph energy is an invariant that is derived from the spectrum of the adjacency matrix of a graph. Graph energy is actually the absolute sum of all the eigenvalues of the adjacency matrix of a graph i.e. E = ∑ i = 1 n λ i , and the Estrada index of a graph G is elaborated as EE G = ∑ i = 1 n e λ i , where, λ 1 , λ 2 , … , λ n are the eigenvalues of the adjacency matrix of a graph. In this paper, energy E G and Estrada index EE G of different molecular structures are obtained and also established inequalities among the exact and estimated values of energies and Estrada index of TUC 4 C 8 nanosh

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25

Rather, Bilal Ahmad, Hilal A. Ganie, Kinkar Chandra Das, and Yilun Shang. "The General Extended Adjacency Eigenvalues of Chain Graphs." Mathematics 12, no. 2 (2024): 192. http://dx.doi.org/10.3390/math12020192.

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In this article, we discuss the spectral properties of the general extended adjacency matrix for chain graphs. In particular, we discuss the eigenvalues of the general extended adjacency matrix of the chain graphs and obtain its general extended adjacency inertia. We obtain bounds for the largest and the smallest general extended adjacency eigenvalues and characterize the extremal graphs. We also obtain a lower bound for the spread of the general extended adjacency matrix. We characterize chain graphs with all the general extended adjacency eigenvalues being simple and chain graphs that are no

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26

Jahanbani, Akbar, Roslan Hasni, Zhibin Du, and Seyed Mahmoud Sheikholeslami. "Spectral Properties with the Difference between Topological Indices in Graphs." Journal of Mathematics 2020 (July 26, 2020): 1–10. http://dx.doi.org/10.1155/2020/6973078.

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Let G be a graph of order n with vertices labeled as v1,v2,…,vn. Let di be the degree of the vertex vi, for i=1,2,…,n. The difference adjacency matrix of G is the square matrix of order n whose i,j entry is equal to di+dj−2−1/didj if the vertices vi and vj of G are adjacent or vivj∈EG and zero otherwise. Since this index is related to the degree of the vertices of the graph, our main tool will be an appropriate matrix, that is, a modification of the classical adjacency matrix involving the degrees of the vertices. In this paper, some properties of its characteristic polynomial are studied. We

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27

Sakunthala, Srinivasan, and Shanmugavel Vimala. "Comparative Study on Different Types of Energies." Indian Journal of Science and Technology 17, no. 28 (2024): 2954–59. https://doi.org/10.17485/IJST/v17i28.1447.

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Abstract <strong>Objectives :</strong> The absolute sum of the eigenvalues is the definition of the graph's energy. In addition to discussing their relationship, this study compares the energy of the Adjacency matrix, Laplacian matrix, Signless Laplacian matrix, and Seidel matrix applied to ten distinct kinds of graphs. In this study, a correlation is established between the energy of graphs and the energy of Edge Antimagic graphs. <strong>Methods:</strong> The technical description of the graph's energy, . An Edge Antimagic graph's energy, identified by (G) = , is the absolute

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28

Ghorbani, Modjtaba, Xueliang Li, Samaneh Zangi, and Najaf Amraei. "On the eigenvalue and energy of extended adjacency matrix." Applied Mathematics and Computation 397 (May 2021): 125939. http://dx.doi.org/10.1016/j.amc.2020.125939.

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29

Pirzada, S., Bilal A. Rather, Hilal A. Ganie та Rezwan ul Shaban. "On α-adjacency energy of graphs and Zagreb index". AKCE International Journal of Graphs and Combinatorics 18, № 1 (2021): 39–46. http://dx.doi.org/10.1080/09728600.2021.1917973.

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30

Khan, Mehtab, Rashid Farooq, and Juan Rada. "Corrigendum to ‘Complex adjacency matrix and energy of digraphs’." Linear and Multilinear Algebra 68, no. 1 (2019): 220–22. http://dx.doi.org/10.1080/03081087.2019.1682806.

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31

Hassan, Zuzan Naaman, and Nihad Titan Sarhan. "The Energy of Conjugacy Classes Graphs of Some Order of Alternating Groups." Journal of University of Raparin 7, no. 4 (2020): 62–71. http://dx.doi.org/10.26750/vol(7).no(4).paper5.

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The energy of a graph , is the sum of all absolute values of the eigen values of the adjacency matrix which is indicated by . An adjacency matrix is a square matrix used to represent of finite graph where the rows and columns consist of 0 or 1-entry depending on the adjacency of the vertices of the graph. The group of even permutations of a finite set is known as an alternating group . The conjugacy class graph is a graph whose vertices are non-central conjugacy classes of a group , where two vertices are connected if their cardinalities are not coprime. In this paper, the conjugacy class of a

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32

Hayat, Sakander, Sunilkumar M. Hosamani, Asad Khan, Ravishankar L. Hutagi, Umesh S. Mujumdar, and Mohammed J. F. Alenazi. "A novel edge-weighted matrix of a graph and its spectral properties with potential applications." AIMS Mathematics 9, no. 9 (2024): 24955–76. http://dx.doi.org/10.3934/math.20241216.

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<p>Regarding a simple graph $ \Gamma $ possessing $ \nu $ vertices ($ \nu $-vertex graph) and $ m $ edges, the vertex-weight and weight of an edge $ e = uv $ are defined as $ w(v_{i}) = d_{ \Gamma}(v_{i}) $ and $ w(e) = d_{ \Gamma}(u)+d_{ \Gamma}(v)-2 $, where $ d_{ \Gamma}(v) $ is the degree of $ v $. This paper puts forward a novel graphical matrix named the edge-weighted adjacency matrix (adjacency of the vertices) $ A_{w}(\Gamma) $ of a graph $ \Gamma $ and is defined in such a way that, for any $ v_{i} $ that is adjacent to $ v_{j} $, its $ (i, j) $-entry equals $ w(e) = d_{ \Gamma}

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33

Macha, Jyoti, Sumedha S. Shinde, and Prema Sunkad. "THE GENERAL SYMMETRIC DEGREE AND GENERAL SYMMETRIC DEGREE ADJACENCY POLYNOMIAL OF A GRAPH AND ITS ENERGY." Advances and Applications in Discrete Mathematics 41, no. 8 (2024): 641–61. http://dx.doi.org/10.17654/0974165824041.

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The spectral graph theory is concerned with the relationship between the spectra of specific matrices associated with a graph and the structural properties of that graph. This paper introduces a general symmetric degree adjacency of a graph G, general symmetric degree of a graph G, and complete weighted graph of a graph. Here we explore its characteristic polynomial using Sachs theorem. We also investigate the bounds for index and energy of general symmetric degree adjacency of a graph. We give two algorithms, first one to find general symmetric degree adjacency of a graph G and second one to

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34

G, Sangeetha, and J. Kavitha. "Results on Graph Energy." Journal of Physics: Conference Series 2332, no. 1 (2022): 012008. http://dx.doi.org/10.1088/1742-6596/2332/1/012008.

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Abstract Adjacency matrix A(G)=[aij] yields the graph energy, which is equal to the addition of absolute values of the eigenvalues G. This research investigates the energy graph class in terms of another graph class after removing a vertex. After deleting a vertex, a relationship between the energy of a complete graph E[kn ] and energy of a splitting graph E(S’ [kn ]) is discovered.

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Das, Parikshit, Sourav Mondal, and Anita Pal. "On Second Zagreb Energy of Graphs." MATCH – Communications in Mathematical and in Computer Chemistry 92, no. 1 (2024): 105–31. http://dx.doi.org/10.46793/match.92-1.105d.

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Chemical structures are transformed into real numbers employing topological indices, which enable numerical computations to substitute pricey wet lab experiments. The spectral properties of topological indices can be investigated by appropriate modification of adjacency matrix. Gutman and Trinajstic, pioneers in the field of chemical graph theory, presented the Zagreb indices, which have governed topological indices research since 1972. The modified adjacency matrix associated to the second Zagreb index (M2) is studied in this work. The second Zagreb energy (ZE2) is generated from this matrix.

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36

Vivik J., Veninstine. "Energy and basic reproduction number of n-Corona graphs prior to order 1." Proyecciones (Antofagasta) 41, no. 4 (2022): 835–54. http://dx.doi.org/10.22199/issn.0717-6279-4694.

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This paper advances the corona product to n times corona in the aspect of increasing and decreasing product of graphs and calibrates its energy and basic reproduction number. The proposed model emanates as a graph with successive generations of complexity, whose structure is constructed as a matrix based on its adjacency. The energy is measured from the sum of the absolute values of the eigenvalues of the adjacency matrix of graph G and the largest eigenvalue is known to be R0. The energy upper bound for increasing and decreasing n-corona product with order 1 of complete graphs are attained.

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37

Rajendra, R., and P. Siva Kota Reddy. "On Tosha-degree of an Edge in a Graph." European Journal of Pure and Applied Mathematics 13, no. 5 (2020): 1097–109. http://dx.doi.org/10.29020/nybg.ejpam.v13i5.3710.

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In an earlier paper, we have introduced the Tosha-degree of an edge in a graph without multiple edges and studied some properties. In this paper, we extend the definition of Tosha-degree of an edge in a graph in which multiple edges are allowed. Also, we introduce the concepts - zero edges in a graph, $T$-line graph of a multigraph, Tosha-adjacency matrix, Tosha-energy, edge-adjacency matrix and edge energy of a graph $G$ and obtain some results.

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38

Filipovski, Slobodan, and Robert Jajcay. "Bounds for the Energy of Graphs." Mathematics 9, no. 14 (2021): 1687. http://dx.doi.org/10.3390/math9141687.

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Let G be a graph on n vertices and m edges, with maximum degree Δ(G) and minimum degree δ(G). Let A be the adjacency matrix of G, and let λ1≥λ2≥…≥λn be the eigenvalues of G. The energy of G, denoted by E(G), is defined as the sum of the absolute values of the eigenvalues of G, that is E(G)=|λ1|+…+|λn|. The energy of G is known to be at least twice the minimum degree of G, E(G)≥2δ(G). Akbari and Hosseinzadeh conjectured that the energy of a graph G whose adjacency matrix is nonsingular is in fact greater than or equal to the sum of the maximum and the minimum degrees of G, i.e., E(G)≥Δ(G)+δ(G).

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Ma, Yamei, Yingjun Ruan, Tingting Xu, Yuting Yao, and Hua Meng. "Short term energy consumption prediction of regional building group based on spatiotemporal graph convolutional network considering spatiotemporal correlation between building nodes." Journal of Physics: Conference Series 3001, no. 1 (2025): 012007. https://doi.org/10.1088/1742-6596/3001/1/012007.

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Abstract With the rapid development of high-performance computing technology, accurate regional building energy consumption prediction based on data-driven is the basis for the refined management of regional energy consumption and energy saving and emission reduction. Owing to climatic conditions, human movement, and other factors, the energy consumption of buildings is influenced not only by their inherent characteristics but also by surrounding buildings. However, there is a lack of a systematic approach to modeling the spatial dependence of regional buildings. Therefore, this study proposed

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40

K., Vimala, and Navetha D. "ENERGY OF A CYCLE AND ITS MIDDLE GRAPH." International Journal of Current Research and Modern Education, Special Issue (August 15, 2017): 92–94. https://doi.org/10.5281/zenodo.843543.

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Let G be a finite, undirected and simple graph. If { } is the set of vertices of G, then the adjacency matrix A(G)=[ ] is an n-by-n matrix where =1 if and are adjacent and =0 otherwise. The energy of a graph ,E(G) is defined as the sum of the absolute values of Eigen values of A(G).Several classes of graphs are known that satisfy the condition E(G)>n ,where n is the number of vertices. This paper contains the energy of the middle graph of the cycle. This paper shows that, if G be a cycle with n vertices and n edges then its middle graph has 2n vertices and 3n edges and the energy of middle

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Redžepović, Izudin, and Ivan Gutman. "Comparing Energy and Sombor Energy - An Empirical Study." Match Communications in Mathematical and in Computer Chemistry 88, no. 1 (2022): 133–40. http://dx.doi.org/10.46793/match.88-1.133r.

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The Sombor index is a recently invented vertex-degree-based topological index, to which a matrix – called Sombor matrix – is associated in a natural manner. The graph energy E(G) is the sum of absolute values of the eigenvalues of the adjacency matrix of the graph G. Analogously, the Sombor energy ESO(G) is the sum of absolute values of the eigenvalues of the Sombor matrix. In this paper, we present computational results on the relations between ESO(G) and E(G) for various classes of (molecular) graphs, and establish the respective regularities. The correlation between ESO(G) and E(G) if found

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D'Souza, S., K. P. Girija та H. J. Gowtham. "Цветовая энергия некоторых кластерных графов". Владикавказский математический журнал, № 2 (24 червня 2021): 51–64. http://dx.doi.org/10.46698/x5522-9720-4842-z.

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Let $G$ be a simple connected graph. The energy of a graph $G$ is defined as sum of the absolute eigenvalues of an adjacency matrix of the graph $G$. It represents a proper generalization of a formula valid for the total $\pi$-electron energy of a conjugated hydrocarbon as calculated by the Huckel molecular orbital (HMO) method in quantum chemistry. A coloring of a graph $G$ is a coloring of its vertices such that no two adjacent vertices share the same color. The minimum number of colors needed for the coloring of a graph $G$ is called the chromatic number of $G$ and is denoted by $\chi(G)$.

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Hameed, Saira, and Uzma Ahmad. "Minimal Energy Tree with 4 Branched Vertices." Open Chemistry 17, no. 1 (2019): 198–205. http://dx.doi.org/10.1515/chem-2019-0013.

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AbstractThe energy of a graph is defined as the sum of absolute values of the eigenvalues of its adjacency matrix. Let Ω(n,4) be the class of all trees of order n and having 4 branched vertices. In this paper, the minimal energy tree in the class Ω(n,4) is found.

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A R, Nagalakshmi. "The Cordial Energy of Some Graphs." Proyecciones (Antofagasta) 43, no. 6 (2024): 1455–71. https://doi.org/10.22199/issn.0717-6279-6403.

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This paper provides a comprehensive investigation into cordial spectra and energy. The study delves into the fundamental principles of cordial labeling, where graph vertices are assigned labels to maintain balanced adjacency. The analysis includes mathematical properties and the interplay between cordial labeling and graph energy. Spectral analysis involving eigenvalues of matrices associated with cordially labeled graphs is explored, offering insights into graph structural characteristics and relationships.

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A., Nagarani, and Vimala S. "Energy of Fuzzy Regular and Graceful Graphs." Asian Research Journal of Mathematics 4, no. 2 (2017): 1–8. https://doi.org/10.9734/ARJOM/2017/33057.

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Energy of graph and energy of fuzzy graph is the sum of the absolute values of the eigen values of adjacency matrix. The concept of energy of fuzzy graph is extended to fuzzy regular, totally regular and graceful graphs in this paper. This paper intends to elaborate about characteristics of eigen values, upper and lower bound of energy.

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Sharafdini, Reza, Rajat Kanti Nath, and Rezvan Darbandi. "Energy of commuting graph of finite AC-groups." Proyecciones (Antofagasta) 41, no. 1 (2022): 263–73. http://dx.doi.org/10.22199/issn.0717-6279-4365.

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Let Γ be a graph with the adjacency matrix A. The energy of Γ is the sum of the absolute values of the eigenvalues of A. In this article we compute the energies of the commuting graphs of some finite groups and discuss some consequences regarding hyperenergetic and borderenergetic graphs.

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Ramane, Harishchandra S., B. Parvathalu, K. Ashoka, and Daneshwari Patil. "On A-energy and S-energy of certain class of graphs." Acta Universitatis Sapientiae, Informatica 13, no. 2 (2021): 195–219. http://dx.doi.org/10.2478/ausi-2021-0009.

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Abstract Let A and S be the adjacency and the Seidel matrix of a graph G respectively. A-energy is the ordinary energy E(G) of a graph G defined as the sum of the absolute values of eigenvalues of A. Analogously, S-energy is the Seidel energy ES(G) of a graph G defined to be the sum of the absolute values of eigenvalues of the Seidel matrix S. In this article, certain class of A-equienergetic and S-equienergetic graphs are presented. Also some linear relations on A-energies and S-energies are given.

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Andjelic, Milica, Tamara Koledin, and Zoran Stanic. "Distance spectrum and energy of graphs with small diameter." Applicable Analysis and Discrete Mathematics 11, no. 1 (2017): 108–22. http://dx.doi.org/10.2298/aadm1701108a.

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In this paper we express the distance spectrum of graphs with small diameter in terms of the eigenvalues of their adjacency matrix. We also compute the distance energy of particular types of graph and determine a sequence of infinite families of distance equienergetic graphs.

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Agudelo Muñetón, Natalia, Agustín Moreno Cañadas, Pedro Fernando Fernández Espinosa, and Isaías David Marín Gaviria. "{0,1}-Brauer Configuration Algebras and Their Applications in Graph Energy Theory." Mathematics 9, no. 23 (2021): 3042. http://dx.doi.org/10.3390/math9233042.

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The energy E(G) of a graph G is the sum of the absolute values of its adjacency matrix. In contrast, the trace norm of a digraph Q, which is the sum of the singular values of the corresponding adjacency matrix, is the oriented version of the energy of a graph. It is worth pointing out that one of the main problems in this theory consists of determining appropriated bounds of these types of energies for significant classes of graphs, digraphs and matrices, provided that, in general, finding out their exact values is a problem of great difficulty. In this paper, the trace norm of a {0,1}-Brauer

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Das, Kinkar Ch, Ivan Gutman, and Boris Furtula. "On spectral radius and energy of extended adjacency matrix of graphs." Applied Mathematics and Computation 296 (March 2017): 116–23. http://dx.doi.org/10.1016/j.amc.2016.10.029.

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