期刊名称：AKCE International Journal of Graphs and Combinatorics
印刷版ISSN：0972-8600
出版年度：2015
卷号：12
期号：2-3
页码：186-192
DOI：10.1016/j.akcej.2015.11.014
语种：English
出版社：Elsevier
摘要：AbstractLetGbe a connected graph with a distance matrixD. TheD-eigenvalues{μ1,μ2,…,…,μp}ofGare the eigenvalues ofDand form the distance spectrum orD-spectrum ofG. Given two graphsGwith vertex set{v1,v2,……,vp}andH, the coronaG∘His defined as the graph obtained by takingpcopies ofHand for eachi, joining theith vertex ofGto all the vertices in theith copy ofH. LetHbe a rooted graph rooted atu. Then the clusterG{H}is defined as the graph obtained by takingpcopies ofHand for eachi, joining theith vertex ofGto the root in theith copy ofH. In this paper we describe the distance spectrum ofG∘H, for a connected distance regular graphGand anyr-regular graphHin terms of the distance spectrum ofGand adjacency spectrum ofH. We also describe the distance spectrum ofG{Kn}, whereGis a connected distance regular graph.
