Results 1 to 10 of about 252,020 (311)
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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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 of a graph and is denoted by . The graph with vertices is called nonhypoenergetic if and hypoenergetic if . Singular graphs are graphs with nullity .
T.K. Mathew Varkey, John K. Rajan
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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 energy, Laplacian energy and $p$-fold graphs
Electronic Journal of Graph Theory and Applications, 2015 For a graph $G$ having adjacency spectrum ($A$-spectrum) $\lambda_n\leq\lambda_{n-1}\leq\cdots\leq\lambda_1$ and Laplacian spectrum ($L$-spectrum) $0=\mu_n\leq\mu_{n-1}\leq\cdots\leq\mu_1$, the energy is defined as $ E(G)=\sum_{i=1}^{n}|\lambda_i|$ and ...
Hilal A Ganie +2 more
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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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Equienergetic chemical trees [PDF]
Journal of the Serbian Chemical Society, 2004 The energy E(G) of a graph G is the sum of the absolute values of the eigenvalues of G. Two graphs, G 1 and G 2, are said to be equienergetic if E(G 1) = E(G 2).We report here the results of the search for pairs of equienergetic acyclic molecular graphs (
Brankov Vladimir +2 more
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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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No Hückel graph is hyperenergetic [PDF]
Journal of the Serbian Chemical Society, 2000 If G is a molecular graph with n vertices and if λ1, λ2, ..., λn are its eigenvalues, then the energy of G is equal to E(G) = |λ1| + |λ2|+ ... + |λn|. If E(G) > 2n - 2, then G is said to be hyperenergetic.
Gutman I. +4 more
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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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Energies, 2022 Sustainable transportation has a significant impact on factors related to urban development and economic development. Therefore, much research is being undertaken to select the best strategies to manage sustainable transportation. Transportation requires
Preeti Devi +7 more
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