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On Laplacian Equienergetic Signed Graphs [PDF]
Journal of Mathematics, 2021 The Laplacian energy of a signed graph is defined as the sum of the distance of its Laplacian eigenvalues from its average degree. Two signed graphs of the same order are said to be Laplacian equienergetic if their Laplacian energies are equal.
Qingyun Tao, Lixin Tao
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Axioms, 2022 The ISI-energy εisi(G) of a graph G=(V,E) is the sum of the absolute values of the eigenvalues of the ISI-matrix C(G)=[cij]n×n in which cij=d(vi)d(vj)d(vi)+d(vj) if vivj∈E(G) and cij=0 otherwise. d(vi) denotes the degree of vertex vi∈V.
fengwei Li
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Distance equienergetic graphs of diameter 4
Examples and CounterexamplesLet Γ1, Γ2 and Γ3 be graphs with pairwise disjoint vertex sets. The graph Θ(Γ1,Γ2,Γ3) is obtained from the graphs Γ1∘Γ3 (the corona product) and Γ2 by joining each vertices of Γ1 in Γ1∘Γ3 with every vertices in Γ2.
B.J. Manjunatha +2 more
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On spectra of variants of the corona of two graphs and some new equienergetic graphs [PDF]
Discussiones Mathematicae - Graph Theory, 2016 Let G and H be two graphs. The join G ∨ H is the graph obtained by joining every vertex of G with every vertex of H. The corona G ○ H is the graph obtained by taking one copy of G and |V (G)| copies of H and joining the i-th vertex of G to every vertex ...
Adiga Chandrashekar, Rakshith B.R.
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On the construction of L-equienergetic graphs [PDF]
AKCE International Journal of Graphs and Combinatorics, 2015 For a graph G with n vertices and m edges, and having Laplacian spectrum μ1,μ2,…,μn and signless Laplacian spectrum μ1+,μ2+,…,μn+, the Laplacian energy and signless Laplacian energy of G are respectively, defined as LE(G)=∑i=1n|μi−2mn| and LE+(G)=∑i=1n ...
S. Pirzada, Hilal A. Ganie
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Upper bounds for the extended energy of graphs and some extended equienergetic graphs [PDF]
Opuscula Mathematica, 2018 In this paper, we give two upper bounds for the extended energy of a graph one in terms of ordinary energy, maximum degree and minimum degree of a graph, and another bound in terms of forgotten index, inverse degree sum, order of a graph and minimum ...
B R Rakshith
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Certain classes of complementary equienergetic graphs [PDF]
Transactions on Combinatorics, 2022 The energy of a graph is the sum of the absolute values of the eigenvalues of a graph. Two graphs are said to be equienergetic if they have same energy.
Harishchandra Ramane +2 more
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Construction of Albertson Cospectral and Albertson Equienergetic Graphs Using Graph Operations
Journal of MathematicsThe energy of a graph is an invariant calculated as the sum of the absolute eigenvalues of its adjacency matrix. This concept extends to various types of energies derived from different graph-related matrices.
Jane Shonon Cutinha +2 more
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Construction of L-equienergetic graphs using some graph operations
AKCE International Journal of Graphs and Combinatorics, 2020 For a graph G with n vertices and m edges, the eigenvalues of its adjacency matrix A(G) are known as eigenvalues of G. The sum of absolute values of eigenvalues of G is called the energy of G.
S K Vaidya
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On Some Topological Indices Defined via the Modified Sombor Matrix [PDF]
Molecules, 2022 Let G be a simple graph with the vertex set V={v1,…,vn} and denote by dvi the degree of the vertex vi. The modified Sombor index of G is the addition of the numbers (dvi2+dvj2)−1/2 over all of the edges vivj of G.
Xuewu Zuo +3 more
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