Spectral characterizations of sun graphs and broken sun graphs
Spectral characterizations of sun graphs and broken sun graphs
复制标题
DOI：
10.46298/dmtcs.456
复制
发表时间：
2009-12
期刊：
影响因子：
--
通讯作者：
Romain Boulet
中科院分区：
文献类型：
--
作者：
Romain Boulet
几个矩阵可以与图相关联，例如邻接矩阵或拉普拉斯矩阵。这些矩阵的谱给出了一些关于图的结构和问题“哪些图由它们的谱决定？”“”一直是代数图论中的一个难题。在这篇文章中，我们通过考虑一些单圈图来扩大已知的由谱决定的图族。一个奇怪的（resp。偶数）太阳是通过将悬挂顶点附加到奇数（或偶数）太阳的每个顶点而获得的图。偶数）循环。一个破太阳是通过删除太阳的悬垂顶点而得到的图。本文证明了一个太阳由它的Laplacian谱决定，一个奇太阳由它的邻接谱决定（对于偶太阳给出了反例），并给出了破碎太阳的一些谱特征。
Several matrices can be associated to a graph such as the adjacency matrix or the Laplacian matrix. The spectrum of these matrices gives some informations about the structure of the graph and the question ''Which graphs are determined by their spectrum?'' remains a difficult problem in algebraic graph theory. In this article we enlarge the known families of graphs determined by their spectrum by considering some unicyclic graphs. An odd (resp. even) sun is a graph obtained by appending a pendant vertex to each vertex of an odd (resp. even) cycle. A broken sun is a graph obtained by deleting pendant vertices of a sun. In this paper we prove that a sun is determined by its Laplacian spectrum, an odd sun is determined by its adjacency spectrum (counter-examples are given for even suns) and we give some spectral characterizations of broken suns.