Results 11 to 20 of about 114 (91)
On comparison between the distance energies of a connected graph [PDF]
HeliyonLet G be a simple connected graph of order n having Wiener index W(G). The distance, distance Laplacian and the distance signless Laplacian energies of G are respectively defined asDE(G)=∑i=1n|υiD|,DLE(G)=∑i=1n|υiL−Tr‾|andDSLE(G)=∑i=1n|υiQ−Tr‾|, where ...
Hilal A. Ganie +2 more
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On the Largest Distance (Signless Laplacian) Eigenvalue of Non-transmission-regular Graphs
The Electronic Journal of Linear Algebra, 2018 Let $G=(V(G),E(G))$ be a $k$-connected graph with $n$ vertices and $m$ edges. Let $D(G)$ be the distance matrix of $G$. Suppose $\lambda_1(D)\geq \cdots \geq \lambda_n(D)$ are the $D$-eigenvalues of $G$. The transmission of $v_i \in V(G)$, denoted by $Tr_G(v_i)$ is defined to be the sum of distances from $v_i$ to all other vertices of $G$, i.e., the ...
Liu, Shuting, Shu, Jinlong, Xue, Jie
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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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Distance (signless) Laplacian spectrum of dumbbell graphs [PDF]
Transactions on Combinatorics, 2023 In this paper, we determine the distance Laplacian and distance signless Laplacian spectrum of generalized wheel graphs and a new class of graphs called dumbbell graphs.
Sakthidevi Kaliyaperumal +1 more
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On the Second-Largest Reciprocal Distance Signless Laplacian Eigenvalue [PDF]
Mathematics, 2021 The signless Laplacian reciprocal distance matrix for a simple connected graph G is defined as RQ(G)=diag(RH(G))+RD(G). Here, RD(G) is the Harary matrix (also called reciprocal distance matrix) while diag(RH(G)) represents the diagonal matrix of the total reciprocal distance vertices.
Maryam Baghipur +3 more
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On the sum of distance signless Laplacian eigenvalues of graphs
Indian Journal of Pure and Applied MathematicsSaleem Khan, S Pirzada, Kinkar Ch Das
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On Extremal Spectral Radii of Uniform Supertrees with Given Independence Number
Discrete Dynamics in Nature and Society, Volume 2022, Issue 1, 2022., 2022 A supertree is a connected and acyclic hypergraph. Denote by Tm,n,α the set of m‐uniform supertrees of order n with independent number α. Focusing on the spectral radius in Tm,n,α, this present completely determines the hypergraphs with maximum spectral radius among all the supertrees with n vertices and independence number α for [m − 1/mn] ≤ α ≤ n − 1,
Lei Zhang +2 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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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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