Some graft transformations and its application on a distance spectrum
Some graft transformations and its application on a distance spectrum
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DOI：
10.1016/j.disc.2011.05.040
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发表时间：
2011-10
期刊：
影响因子：
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通讯作者：
Guanglong Yu;Yarong Wu;Yajie Zhang;Jinlong Shu
中科院分区：
文献类型：
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作者：
Guanglong Yu;Yarong Wu;Yajie Zhang;Jinlong Shu
设D(G)=(di，j)n×n表示n阶连通图G的距离矩阵，其中di等于图G中v i与v j之间的距离，D(G)的最大特征值称为图G的距离谱半径，记为ϱ(G).本文给出了一些降低和增加ϱ(G)的嫁接变换，并证明了图S n‘(由n(n不等于4，5)个顶点上的S星通过增加一条连接两个悬挂点的边得到的)在n个顶点的单圈图中具有最小的距离谱半径，而Pn’(由三角形K3附加一个悬挂路Pn−3得到的)在n个顶点的单圈图中具有最大的距离谱半径.
Abstract Let D (G)=(d i, j) n× n denote the distance matrix of a connected graph G with order n, where d i j is equal to the distance between v i and v j in G. The largest eigenvalue of D (G) is called the distance spectral radius of graph G, denoted by ϱ (G). In this paper, we give some graft transformations that decrease and increase ϱ (G) and prove that the graph S n′(obtained from the star S n on n (n is not equal to 4, 5) vertices by adding an edge connecting two pendent vertices) has minimal distance spectral radius among unicyclic graphs on n vertices; while P n′(obtained from a triangle K 3 by attaching pendent path P n− 3 to one of its vertices) has maximal distance spectral radius among unicyclic graphs on n vertices.