Results 11 to 20 of about 81 (63)
Computing the reciprocal distance signless Laplacian eigenvalues and energy of graphs
Le Matematiche, 2019 Summary: In this paper, we study the eigenvalues of the reciprocal distance signless Laplacian matrix of a connected graph and obtain some bounds for the maximum eigenvalue of this matrix. We also focus on bipartite graphs and find some bounds for the spectral radius of the reciprocal distance signless Laplacian matrix of this class of graphs. Moreover,
A. Alhevaz, M. Baghipur, H.S. Ramane
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Spectral Properties of the Harary Signless Laplacian and Harary Incidence Energy
MathematicsLet X be a partitioned matrix and let B its equitable quotient matrix. Consider a simple, undirected, connected graph G of order n. In this paper, we employ a technique based on quotient matrices derived from block-partitioned structures to establish new
Luis Medina +2 more
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ENERGY OF NON-COPRIME GRAPH ON MODULO GROUP
BarekengA graph is a mathematical structure consisting of a non-empty set of vertices and a set of edges connecting these vertices. In recent years, extensive research on graphs has been conducted, with one of the intriguing topics being the representation of ...
Gusti Yogananda Karang +2 more
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Some bounds for distance signless Laplacian energy-like invariant of networks
Carpathian Mathematical PublicationsFor a graph or network $G$, denote by $D(G)$ the distance matrix and $Tr(G)$ the diagonal matrix of vertex transmissions. The distance signless Laplacian matrix of $G$ is $D^{Q}(G)=Tr(G)+D(G)$. We introduce the distance signless Laplacian energy-like invariant as $DEL(G)=\sum_{i=1}^{n}\sqrt{\rho_{i}}$, where $\rho_{1}\geq\rho_{2}\geq \dots\geq \rho_{n}$
A. Alhevaz +3 more
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New Bounds for the Generalized Distance Spectral Radius/Energy of Graphs
Mathematical Problems in Engineering, Volume 2022, Issue 1, 2022., 2022 Let G be a simple connected graph with vertex set V(G) = {v1, v2, …, vn} and dvi be the degree of the vertex vi. Let D(G) be the distance matrix and Tr(G) be the diagonal matrix of the vertex transmissions of G. The generalized distance matrix of G is defined as Dα(G) = αTr(G) + (1 − α)D(G), where 0 ≤ α ≤ 1. If λ1, λ2, …, λn are the eigenvalues of Dα(G)
Yuzheng Ma +3 more
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On Laplacian Equienergetic Signed Graphs
Journal of Mathematics, Volume 2021, Issue 1, 2021., 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. In this paper, we present several infinite families of Laplacian equienergetic signed graphs.
Qingyun Tao, Lixin Tao, Yongqiang Fu
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Hamilton Connectivity of Convex Polytopes with Applications to Their Detour Index
Complexity, Volume 2021, Issue 1, 2021., 2021 A connected graph is called Hamilton‐connected if there exists a Hamiltonian path between any pair of its vertices. Determining whether a graph is Hamilton‐connected is an NP‐complete problem. Hamiltonian and Hamilton‐connected graphs have diverse applications in computer science and electrical engineering.
Sakander Hayat +4 more
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Some Chemistry Indices of Clique‐Inserted Graph of a Strongly Regular Graph
Complexity, Volume 2021, Issue 1, 2021., 2021 In this paper, we give the relation between the spectrum of strongly regular graph and its clique‐inserted graph. The Laplacian spectrum and the signless Laplacian spectrum of clique‐inserted graph of strongly regular graph are calculated. We also give formulae expressing the energy, Kirchoff index, and the number of spanning trees of clique‐inserted ...
Chun-Li Kan +4 more
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On distance Laplacian energy in terms of graph invariants
, 2023 summary:For a simple connected graph $G$ of order $n$ having distance Laplacian eigenvalues $ \rho ^{L}_{1}\geq \rho ^{L}_{2}\geq \cdots \geq \rho ^{L}_{n}$, the distance Laplacian energy ${\rm DLE} (G)$ is defined as ${\rm DLE} (G)=\sum _{i=1}^{n}|\rho ^
Rather, Bilal A. +3 more
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Bounds on the α‐Distance Energy and α‐Distance Estrada Index of Graphs
Discrete Dynamics in Nature and Society, Volume 2020, Issue 1, 2020., 2020 Let G be a simple undirected connected graph, then Dα(G) = αTr(G) + (1 − α)D(G) is called the α‐distance matrix of G, where α ∈ [0,1], D(G) is the distance matrix of G, and Tr(G) is the vertex transmission diagonal matrix of G. In this paper, we study some bounds on the α‐distance energy and α‐distance Estrada index of G.
Yang Yang +3 more
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