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Discrete Applied Mathematics, 2023 We study the graph energy from a cooperative game viewpoint. We introduce \emph{the graph energy game} and show various properties. In particular, we see that it is a superadditive game and that the energy of a vertex, as defined in Arizmendi and Juarez-Romero (2018), belongs to the core of the game.
Gerardo Arizmendi, Octavio Arizmendi
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The matching energy of a graph
Discrete Applied Mathematics, 2012 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ivan Gutman, Stephan Wagner
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On the spectrum and energy of singular graphs [PDF]
AKCE International Journal of Graphs and Combinatorics, 2019 Energy of a graph is defined as the sum of the absolute values of the eigenvalues of the adjacency matrix A(G)of a graph Gand is denoted by E(G). The graph G with n vertices is called nonhypoenergetic if E(G)≥nand hypoenergetic if E(G)0. In this paper we
T.K. Mathew Varkey, John K. Rajan
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Bounds for the Energy of Graphs [PDF]
Mathematics, 2021 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|.
Slobodan Filipovski, Robert Jajcay
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Relating graph energy with vertex-degree-based energies [PDF]
Vojnotehnički Glasnik, 2020 Introduction/purpose: The paper presents numerous vertex-degree-based graph invariants considered in the literature. A matrix can be associated to each of these invariants.
Ivan Gutman
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Smoothness of Graph Energy in Chemical Graphs
Mathematics, 2023 The energy of a graph G as a chemical concept leading to HMO theory was introduced by Hückel in 1931 and developed into a mathematical interpretation many years later when Gutman in 1978 gave his famous definition of the graph energy as the sum of the absolute values of the eigenvalues of the adjacency matrix of G.
Katja Zemljič, Petra Žigert Pleteršek
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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 ...
Chandrashekar Adiga, B. R. Rakshith
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Asymptotic energy of connected cubic circulant graphs
AKCE International Journal of Graphs and Combinatorics, 2021 In this article, we compute the oblique asymptote of the energy function for all connected cubic circulant graphs. Moreover, we show that this oblique asymptote is an upper bound for the energies of two of the subclasses of Möbius ladder graphs and lower
Alper Bulut, Ilhan Hacioglu
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Randić Incidence Energy of Graphs [PDF]
Transactions on Combinatorics, 2014 Let $G$ be a simple graph with vertex set $V(G) = \{v_1, v_2,\ldots, v_n\}$ and edge set $E(G) = \{e_1, e_2,\ldots, e_m\}$. Similar to the Randić matrix, here we introduce the Randić incidence matrix of a graph $G$, denoted by $I_R(G)$, which is defined as the $n\times m$ matrix whose $(i, j)$-entry is $(d_i)^{-\frac{1}{2}}$ if $v_i$ is incident to ...
Gu, Ran, Huang, Fei, Li, Xueliang
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More Equienergetic Signed Graphs [PDF]
Mathematics Interdisciplinary Research, 2017 The energy of signed graph is the sum of the absolute values of the eigenvalues of its adjacency matrix. Two signed graphs are said to be equienergetic if they have same energy.
Harishchandra S. Ramane +1 more
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