Results 1 to 10 of about 236,543 (259)
Spectral Applications of Vertex-Clique Incidence Matrices Associated with a Graph
Mathematics, 2023 Using the notions of clique partitions and edge clique covers of graphs, we consider the corresponding incidence structures. This connection furnishes lower bounds on the negative eigenvalues and their multiplicities associated with the adjacency matrix,
Shaun Fallat, Seyed Ahmad Mojallal
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Bicyclic molecular graphs with the greatest energy [PDF]
Journal of the Serbian Chemical Society, 2008 The molecular graph Qn is obtained by attaching hexagons to the end vertices of the path graph Pn-12. Earlier empirical studies indicated that Qn has greatest energy among all bicyclic n-vertex (molecular) graphs.
Furtula Boris +2 more
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Oboudi-Type Bounds for Graph Energy [PDF]
Mathematics Interdisciplinary Research, 2019 The graph energy is the sum of absolute values of the eigenvalues of the (0, 1)-adjacency matrix. Oboudi recently obtained lower bounds for graph energy, depending on the largest and smallest graph eigenvalue. In this paper, a few more Oboudi-type bounds
Ivan Gutman
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Bounds for the Hückel Energy of a Graph [PDF]
The Electronic Journal of Combinatorics, 2009 Let $G$ be a graph on $n$ vertices with $r := \lfloor n/2 \rfloor$ and let $\lambda _1 \geq\cdots\geq \lambda _{n} $ be adjacency eigenvalues of $G$. Then the Hückel energy of $G$, HE($G$), is defined as $${\rm HE}(G) = \cases{ \displaystyle \; 2\sum_{i=1}^{r} \lambda_i, & \hbox{if $n= 2r$;} \cr \displaystyle \; 2\sum_{i=1}^{\phantom{l}r ...
Ebrahim Ghorbani +2 more
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Energy and Randić energy of special graphs
Proyecciones (Antofagasta), 2022 In this paper, we determine the Randić energy of the m-splitting graph, the m-shadow graph and the m-duplicate graph of a given graph, m being an arbitrary integer. Our results allow the construction of an infinite sequence of graphs having the same Randić energy. Further, we determine some graph invariants like the degree Kirchhoff index, the Kemeny’s
Jahfar, T. K., Chithra, A. V.
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Novel Concept of Energy in Bipolar Single-Valued Neutrosophic Graphs with Applications
Axioms, 2021 The energy of a graph is defined as the sum of the absolute values of its eigenvalues. Recently, there has been a lot of interest in graph energy research.
Siti Nurul Fitriah Mohamad +3 more
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Advances in Applied Mathematics, 2001 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jack H. Koolen, Vincent Moulton
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{0,1}-Brauer Configuration Algebras and Their Applications in Graph Energy Theory
Mathematics, 2021 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 ...
Natalia Agudelo Muñetón +3 more
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Graph Energies of Egocentric Networks and Their Correlation with Vertex Centrality Measures
Entropy, 2018 Graph energy is the energy of the matrix representation of the graph, where the energy of a matrix is the sum of singular values of the matrix. Depending on the definition of a matrix, one can contemplate graph energy, Randić energy, Laplacian energy ...
Mikołaj Morzy, Tomasz Kajdanowicz
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On Energy and Laplacian Energy of Graphs
The Electronic Journal of Linear Algebra, 2016 Let $G=(V,E)$ be a simple graph of order $n$ with $m$ edges. The energy of a graph $G$, denoted by $\mathcal{E}(G)$, is defined as the sum of the absolute values of all eigenvalues of $G$. The Laplacian energy of the graph $G$ is defined as \[ LE = LE(G)=\sum^n_{i=1}\left|\mu_i-\frac{2m}{n}\right| \] where $\mu_1,\,\mu_2,\,\ldots,\,\mu_{n-1 ...
Das, Kinkar Ch., Mojalal, Seyed Ahmad
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