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An analog of Matrix Tree Theorem for signless Laplacians [PDF]
Linear Algebra and its Applications, 2019 A spanning tree of a graph is a connected subgraph on all vertices with the minimum number of edges. The number of spanning trees in a graph $G$ is given by Matrix Tree Theorem in terms of principal minors of Laplacian matrix of $G$. We show a similar combinatorial interpretation for principal minors of signless Laplacian $Q$.
Keivan Hassani Monfared, Sudipta Mallik
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Seidel Signless Laplacian Energy of Graphs [PDF]
Mathematics Interdisciplinary Research, 2017 Let S(G) be the Seidel matrix of a graph G of order n and let DS(G)=diag(n-1-2d1, n-1-2d2,..., n-1-2dn) be the diagonal matrix with d_i denoting the degree of a vertex v_i in G.
Harishchandra Ramane +3 more
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Forest matrices around the Laplacian matrix
Linear Algebra and its Applications, 2002 19 pages, presented at the Edinburgh (2001) Conference on Algebraic Graph ...
Chebotarev, Pavel, Agaev, Rafig
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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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The Distance Laplacian Spectral Radius of Clique Trees
Discrete Dynamics in Nature and Society, 2020 The distance Laplacian matrix of a connected graph G is defined as ℒG=TrG−DG, where DG is the distance matrix of G and TrG is the diagonal matrix of vertex transmissions of G.
Xiaoling Zhang, Jiajia Zhou
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On Eccentricity Version of Laplacian Energy of a Graph [PDF]
Mathematics Interdisciplinary Research, 2017 The energy of a graph G is equal to the sum of absolute values of the eigenvalues of the adjacency matrix of G, whereas the Laplacian energy of a graph G is equal to the sum of the absolute value of the difference between the eigenvalues of the Laplacian
Nilanjan De
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On the Adjacency, Laplacian, and Signless Laplacian Spectrum of Coalescence of Complete Graphs
Journal of Mathematics, 2016 Coalescence as one of the operations on a pair of graphs is significant due to its simple form of chromatic polynomial. The adjacency matrix, Laplacian matrix, and signless Laplacian matrix are common matrices usually considered for discussion under ...
S. R. Jog, Raju Kotambari
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On Minimum Algebraic Connectivity of Tricyclic Graphs [PDF]
Mathematics Interdisciplinary ResearchConsider a simple, undirected graph $ G=(V,E)$, where $A$ represents the adjacency matrix and $Q$ represents the Laplacian matrix of $G$. The second smallest eigenvalue of Laplacian matrix of $G$ is called the algebraic connectivity of $G$.
Hassan Taheri, Gholam Hossein Fath-Tabar
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MathematicsFor network graphs, numerous graph features are intimately linked to eigenvalues of the Laplacian matrix, such as connectivity and diameter. Thus, it is very important to solve eigenvalues of the Laplacian matrix for graphs.
Changlei Zhan, Xiangyu Li, Jie Chen
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Signless Laplacian determinations of some graphs with independent edges
Karpatsʹkì Matematičnì Publìkacìï, 2018 Let $G$ be a simple undirected graph. Then the signless Laplacian matrix of $G$ is defined as $D_G + A_G$ in which $D_G$ and $A_G$ denote the degree matrix and the adjacency matrix of $G$, respectively.
R. Sharafdini, A.Z. Abdian
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