共查询到20条相似文献,搜索用时 15 毫秒
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On the spectral radius of unicyclic graphs with fixed diameter 总被引:1,自引:0,他引:1
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Let GB(n,d) be the set of bipartite graphs with order n and diameter d. This paper characterizes the extremal graph with the maximal spectral radius in GB(n,d). Furthermore, the maximal spectral radius is a decreasing function on d. At last, bipartite graphs with the second largest spectral radius are determined. 相似文献
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Xianya Geng 《Linear and Multilinear Algebra》2013,61(1):41-56
A tricyclic graph is a connected graph with n vertices and n + 2 edges. In this article, we determine graphs with the largest spectral radius among the n-vertex tricyclic graphs with given diameter d. 相似文献
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In this paper, we give some results on Laplacian spectral radius of graphs with cut vertices, and as their applications, we also determine the unique graph with the largest Laplacian spectral radius among all unicyclic graphs with n vertices and diameter d, 3?d?n−3. 相似文献
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Walks and the spectral radius of graphs 总被引:1,自引:0,他引:1
Vladimir Nikiforov 《Linear algebra and its applications》2006,418(1):257-268
Given a graph G, write μ(G) for the largest eigenvalue of its adjacency matrix, ω(G) for its clique number, and wk(G) for the number of its k-walks. We prove that the inequalities
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R.H Johnson 《Journal of Combinatorial Theory, Series B》1974,17(2):188-198
This paper develops some properties of simple blocks—block graphs which are determined up to isomorphism by the degrees of their vertices. It is first shown that if G is a simple block graph on six or more points, then G cannot be minimal or critical and must contain a triangle—have girth three.Then the most useful necessary conditions for a graph to be simple are established; if a graph is simple, it has diameter less than or equal to three and dradius less than or equal to two. 相似文献
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One common problem in spectral graph theory is to determine which graphs, under some prescribed constraints, maximize or minimize the spectral radius of the adjacency matrix. Here we consider minimizers in the set of bidegreed, or biregular, graphs with pendant vertices and given degree sequence. In this setting, we consider a particular graph perturbation whose effect is to decrease the spectral radius. Hence we restrict the structure of minimizers for k-cyclic degree sequences. 相似文献
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Shmuel Friedland 《Linear and Multilinear Algebra》1993,34(1):33-40
We give lower and upper bounds on the spectral radius of directed Eulerian multigraphs and undirected multigraphs. 相似文献
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José A. de la Peña 《Linear and Multilinear Algebra》2013,61(7):641-649
A cleavage of a finite graph G is a morphism f : H → G of graphs such that if P is the m × n characteristic matrix defined as P ik = 1 if i ∈ f ?1(k), otherwise = 0, then A(H)P ≤ PA(G), where A(G) and A(H) are the adjacency matrices of G and H, respectively. This concept generalizes induced subgraphs, quotients of graphs, Galois covers, path-tree graphs and others. We show that for spectral radii we have the inequality ρ(H) ≤ ρ(G). Equality holds only in case f : H → G is an equivariant quotient and H has isoperimetric constant i(H) = 0. 相似文献
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The Laplacian spectral radius of a graph is the largest eigenvalue of the associated Laplacian matrix. In this paper, we improve
Shi’s upper bound for the Laplacian spectral radius of irregular graphs and present some new bounds for the Laplacian spectral
radius of some classes of graphs. 相似文献
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Ling Sheng Shi 《数学学报(英文版)》2013,29(2):281-286
It was conjectured by Li and Feng in 1979 that the unicyclic graph formed by a cycle of order g linking to an endvertex of a path of length k minimizes the spectral radius of all unicyclic graphs of order g + k and girth g. In 1987, Cao proved that this conjecture is true for k ≥ g(g 2)/8 and false for k = 2 and sufficiently large g. In this note, we show that g 12 suffices for the counterexample and give more counterexamples with large girth for any integer k 1. 相似文献
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Ji-ming Guo 《应用数学学报(英文版)》2008,24(2):289-296
In this paper, sharp upper bounds for the Laplacian spectral radius and the spectral radius of graphs are given, respectively. We show that some known bounds can be obtained from our bounds. For a bipartite graph G, we also present sharp lower bounds for the Laplacian spectral radius and the spectral radius, respectively. 相似文献
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Huiqiu Lin 《Linear and Multilinear Algebra》2013,61(4):442-447
Let D(G) denote the distance matrix of a connected graph G. The largest eigenvalue of D(G) is called the distance spectral radius of a graph G, denoted by ?(G). In this article, we give sharp upper and lower bounds for the distance spectral radius and characterize those graphs for which these bounds are best possible. 相似文献
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Liang Lin 《Linear algebra and its applications》2008,428(4):973-977
Let G be an n-vertex (n?3) simple graph embeddable on a surface of Euler genus γ (the number of crosscaps plus twice the number of handles). Denote by Δ the maximum degree of G. In this paper, we first present two upper bounds on the Laplacian spectral radius of G as follows:
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Shu-Guang Guo 《Linear algebra and its applications》2007,422(1):119-132
Bicyclic graphs are connected graphs in which the number of edges equals the number of vertices plus one. In this paper we determine the graph with the largest spectral radius among all bicyclic graphs with n vertices and diameter d. As an application, we give first three graphs among all bicyclic graphs on n vertices, ordered according to their spectral radii in decreasing order. 相似文献
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In this paper, we determine the unique graph with minimum distance spectral radius among all connected bipartite graphs of order with a given matching number. Moreover, we characterize the graphs with minimal distance spectral radius in the class of all connected bipartite graphs with a given vertex connectivity. 相似文献
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