Laplacian spectral characterization of some double starlike trees
Laplacian spectral characterization of some double starlike trees
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DOI：
10.11990/jheu.201409027
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发表时间：
2012-05
期刊：
影响因子：
--
通讯作者：
Pengli Lu;Xiaogang Liu
中科院分区：
文献类型：
--
作者：
Pengli Lu;Xiaogang Liu
AbstractA tree is called double starlike if it has exactly two vertices of degree greater than two.Let H(p,n,q) denote the double starlike tree obtained by attaching p pendant vertices toone pendant vertex of the path P n and q pendant vertices to the other pendant vertex of P n .In this paper, we prove that H(p,n,q) is determined by its Laplacian spectrum.keywords: Adjacency spectrum; Laplacian spectrum; A-cospectral graphs; L-cospectralgraphs; Line graphAMS Classifications: 05C50 1 Introduction All graphs considered in this paper are simple and undirected. Let G = (V(G),E(G)) be a graphwith vertex set V(G) = {v 1 ,v 2 ,...,v n } and edge set E(G), where v 1 ,v 2 ,...,v n are indexed inthe non-increasing order of degrees. Let d i = d i (G) = d G (v i ) be the degree of the vertex v i , anddeg(G) = (d 1 ,d 2 ,...,d n )the non-increasing degree sequence of G. The adjacencymatrixof G, denoted by A(G), is the n×n matrix whose (i,j)-entry is 1 if v i and v j are adjacent and 0 otherwise. We call L(G) = D(G)−A(G) the Laplacian matrix of G, where D(G) is the n × n diagonal matrix with d
