Results 31 to 40 of about 1,304 (147)
A study on determination of some graphs by Laplacian and signless Laplacian permanental polynomials
AKCE International Journal of Graphs and Combinatorics, 2023 The permanent of an n × n matrix [Formula: see text] is defined as [Formula: see text] where the sum is taken over all permutations σ of [Formula: see text] The permanental polynomial of M, denoted by [Formula: see text] is [Formula: see text] where In ...
Aqib Khan +2 more
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(Generalized) Incidence and Laplacian‐Like Energies
Journal of Mathematics, Volume 2023, Issue 1, 2023., 2023 In this study, for graph Γ with r connected components (also for connected nonbipartite and connected bipartite graphs) and a real number ε(≠0,1), we found generalized and improved bounds for the sum of ε‐th powers of Laplacian and signless Laplacian eigenvalues of Γ.
A. Dilek Maden +2 more
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Two Kinds of Laplacian Spectra and Degree Kirchhoff Index of the Weighted Corona Networks
Journal of Mathematics, Volume 2022, Issue 1, 2022., 2022 Recently, the study related to network has aroused wide attention of the scientific community. Many problems can be usefully represented by corona graphs or networks. Meanwhile, the weight is a vital factor in characterizing some properties of real networks.
Haiqin Liu, Yanling Shao, Azhar Hussain
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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
wiley +1 more source
Spectral Sufficient Conditions on Pancyclic Graphs
Complexity, Volume 2021, Issue 1, 2021., 2021 A pancyclic graph of order n is a graph with cycles of all possible lengths from 3 to n. In fact, it is NP‐complete that deciding whether a graph is pancyclic. Because the spectrum of graphs is convenient to be calculated, in this study, we try to use the spectral theory of graphs to study this problem and give some sufficient conditions for a graph to
Guidong Yu +4 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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Sufficient Conditions for Graphs to Be k‐Connected, Maximally Connected, and Super‐Connected
Complexity, Volume 2021, Issue 1, 2021., 2021 Let G be a connected graph with minimum degree δ(G) and vertex‐connectivity κ(G). The graph G is k‐connected if κ(G) ≥ k, maximally connected if κ(G) = δ(G), and super‐connected if every minimum vertex‐cut isolates a vertex of minimum degree. In this paper, we present sufficient conditions for a graph with given minimum degree to be k‐connected ...
Zhen-Mu Hong +4 more
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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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The Signless Laplacian Estrada Index of Unicyclic Graphs [PDF]
Mathematics Interdisciplinary Research, 2017 For a simple graph G, the signless Laplacian Estrada index is defined as SLEE(G)=∑ni=1eqi, where q1, q2,..., qn are the eigenvalues of the signless Laplacian matrix of G.
Hamid Reza Ellahi +3 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
wiley +1 more source