172 research outputs found

    Spanning k-trees and distance spectral radius in graphs

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    Let k2k\geq2 be an integer. A tree TT is called a kk-tree if dT(v)kd_T(v)\leq k for each vV(T)v\in V(T), that is, the maximum degree of a kk-tree is at most kk. Let λ1(D(G))\lambda_1(D(G)) denote the distance spectral radius in GG, where D(G)D(G) denotes the distance matrix of GG. In this paper, we verify a upper bound for λ1(D(G))\lambda_1(D(G)) in a connected graph GG to guarantee the existence of a spanning kk-tree in GG.Comment: 11 page

    On the Signless Laplacian Spectral Radius of Bicyclic Graphs with Perfect Matchings

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    The graph with the largest signless Laplacian spectral radius among all bicyclic graphs with perfect matchings is determined

    On Some Spectral Invariants of Graphs

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    图谱理论是代数图论的一个重要研究课题,它在量子化学、物理学、计算机科学、通信网络以及信息科学中均有非常重要的应用.图谱理论主要涉及图的邻接谱和Laplacian谱的研究,其研究的主要途径是通过图的矩阵(主要是邻接矩阵和Laplacian矩阵)表示,运用线性代数、矩阵理论等代数工具和技巧并结合图论与组合学的理论和方法,建立图的拓扑结构,特别是反映图的结构性质的各种不变量与图的代数不变量(主要是一些谱不变量)之间的联系. 图的预解Estrada指标、Laplacian谱半径及Laplacian特征值幂和是图的三类有着广泛应用背景的谱不变量.本文首先综述了这三类谱不变量的相关背景及研究进展,然...The spectral graph theory is one of the main branches in algebraic graph theory. There are a lot of important applications in the fields of quantum chemistry, physics, computer science, communication network and information science. It is mainly concerned with the adjacency spectrum and the Laplacian spectrum. The principal approach for this research is by using the matrix (mainly the adjacency ma...学位:理学博士院系专业:数学科学学院数学与应用数学系_应用数学学号:1902009015361
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