Results 51 to 60 of about 2,494 (128)
Prime Graphs of Polynomials and Power Series Over Noncommutative Rings
International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.The prime graph PG(R) of a ring R is a graph whose vertex set consists of all elements of R. Two elements x, y ∈ R are adjacent in the graph if and only if xRy = 0 or yRx = 0. An element a ∈ R is called a strong zero divisor in R if 〈a〉〈b〉 = 0 or 〈b〉〈a〉 = 0 for some nonzero element b ∈ R. The set of all strong zero divisors is denoted by S(R).
Walaa Obaidallah Alqarafi +3 more
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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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Turán’s Theorem Implies Stanley’s Bound
Discussiones Mathematicae Graph Theory, 2020 Let G be a graph with m edges and let ρ be the largest eigenvalue of its adjacency matrix.
Nikiforov V.
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Spectra of some special bipartite graphs
, 2017 LetG D .P;Q/ be a bipartite graph andG be a graph obtained by joining each vertex of P and Q with m and s new vertices respectively. We obtain the characteristic, Laplacian and signless Laplacian polynomial of G. As an application, we give a simple proof
A. F. Laali, H. Javadi
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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
Graphs whose Laplacian eigenvalues are almost all 1 or 2
Special MatricesWe explicitly determine all connected graphs whose Laplacian matrices have at most four eigenvalues different from 1 and 2.
Mohammadian Ali, Xu Shanshan
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Open problems on graph eigenvalues studied with AutoGraphiX
EURO Journal on Computational Optimization, 2013 Since the late forties of the last century, methods of operations research have been extensively used to solve problems in graph theory, and graph theory has been extensively used to model operations research problems and to solve optimization problems ...
Mustapha Aouchiche +2 more
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On Singular Signed Graphs with Nullspace Spanned by a Full Vector: Signed Nut Graphs
Discussiones Mathematicae Graph Theory, 2022 A signed graph has edge weights drawn from the set {+1, −1}, and is sign-balanced if it is equivalent to an unsigned graph under the operation of sign switching; otherwise it is sign-unbalanced.
Bašić Nino +3 more
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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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On the α-Spectral Radius of Uniform Hypergraphs
Discussiones Mathematicae Graph Theory, 2020 For 0 ≤ α ---lt--- 1 and a uniform hypergraph G, the α-spectral radius of G is the largest H-eigenvalue of αD(G)+(1−α)A(G), where D(G) and A(G) are the diagonal tensor of degrees and the adjacency tensor of G, respectively. We give upper bounds for the α-
Guo Haiyan, Zhou Bo
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