Results 41 to 50 of about 2,691 (126)
Distance spectrum and energy of graphs with small diameter
, 2017 λ1(G) ≥ λ2(G) ≥ · · · ≥ λn(G), are then just the roots of ΦG, and the spectrum of G, denoted by ΣG, is the multiset of its eigenvalues. If G is connected then its distance matrix is an n × n matrix DG = (dij), where dij is the distance (length of a ...
Milica Andjelic +2 more
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On the Maximum SC Index of Chemical Unicyclic Graphs
Journal of Mathematics, Volume 2025, Issue 1, 2025.The sum‐connectivity (SC) index of a graph G is defined as SCG=∑μν∈EG1/Θμ+Θν, where Θμ denotes the vertex degree of μ in G. In this paper, the fourth largest value of SC index for the chemical unicyclic graphs of order n ≥ 7 is determined.
Hui-Yan Cheng +3 more
wiley +1 more source
On First Hermitian-Zagreb Matrix and Hermitian-Zagreb Energy
International Journal of Scientific Research in Mathematical and Statistical Sciences, 2018 A mixed graph is a graph with edges and arcs, which can be considered as a combination of an undirected graph and a directed graph. In this paper we propose a Hermitian matrix for mixed graphs which is a modified version of the classical adjacency matrix
A. Bharali
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Graphic and Cographic Г-Extensions of Binary Matroids
Discussiones Mathematicae Graph Theory, 2018 Slater introduced the point-addition operation on graphs to characterize 4-connected graphs. The Г-extension operation on binary matroids is a generalization of the point-addition operation. In general, under the Г-extension operation the properties like
Borse Y.M., Mundhe Ganesh
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The normalized distance Laplacian
Special Matrices, 2021 The distance matrix 𝒟(G) of a connected graph G is the matrix containing the pairwise distances between vertices. The transmission of a vertex vi in G is the sum of the distances from vi to all other vertices and T(G) is the diagonal matrix of ...
Reinhart Carolyn
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Bounds for Laplacian-type graph energies
, 2015 Let G be an undirected simple and connected graph with n vertices .n 3/ and m edges. Denote by 1 2 n 1 > n D 0, 1 2 n , and 1 2 n 1 > n D 0 , respectively, the Laplacian, signless Laplacian, and normalized Laplacian eigenvalues of G. The Laplacian energy,
I. Gutman +2 more
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Degree Subtraction Adjacency Eigenvalues and Energy of Graphs Obtained From Regular Graphs
Open Journal of Discrete Applied Mathematics, 2018 Let V (G) = {v1, v2, . . . , vn} be the vertex set of G and let dG(vi) be the degree of a vertex vi in G. The degree subtraction adjacency matrix of G is a square matrix DSA(G) = [dij ], in which dij = dG(vi) − dG(vj), if vi is adjacent to vj and dij = 0,
H. Ramane, Hemaraddi N. Maraddi
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On the sum of the two largest Laplacian eigenvalues of trees
, 2014 For S(T), the sum of the two largest Laplacian eigenvalues of a tree T, an upper bound is obtained. Moreover, among all trees with n≥4 vertices, the unique tree which attains the maximal value of S(T) is determined.MSC:05C50.
Mei Guan, M. Zhai, Yongfeng Wu
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Complexity of graphs generated by wheel graph and their asymptotic limits
Journal of the Egyptian Mathematical Society, 2017 The literature is very rich with works deal with the enumerating the spanning trees in any graph G since the pioneer Kirchhoff (1847). Generally, the number of spanning trees in a graph can be acquired by directly calculating an associated determinant ...
S.N. Daoud
doaj
A new upper bound on the largest normalized Laplacian eigenvalue
, 2013 Let G be a simple undirected connected graph on n vertices. Suppose that the vertices of G are labelled 1,2, . . . ,n. Let di be the degree of the vertex i.
O. Rojo, R. Soto
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