Authors: Indulal, Gopalapillai
Stevanović, Dragan 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: The distance spectrum of corona and cluster of two graphs
Journal: AKCE International Journal of Graphs and Combinatorics
Volume: 12
Issue: 2-3
First page: 186
Last page: 192
Issue Date: 1-Nov-2015
ISSN: 0972-8600
DOI: 10.1016/j.akcej.2015.11.014
Abstract: 
Let G be a connected graph with a distance matrix D. The D-eigenvalues {μ1, μ2, . . ., . . ., μp} of G are the eigenvalues of D and form the distance spectrum or D-spectrum of G. Given two graphs G with vertex set {v1,v2,. . .. . .,vp} and H, the corona G-H is defined as the graph obtained by taking p copies of H and for each i, joining the ith vertex of G to all the vertices in the ith copy of H. Let H be a rooted graph rooted at u. Then the cluster G{H} is defined as the graph obtained by taking p copies of H and for each i, joining the ith vertex of G to the root in the ith copy of H. In this paper we describe the distance spectrum of G-H, for a connected distance regular graph G and any r-regular graph H in terms of the distance spectrum of G and adjacency spectrum of H. We also describe the distance spectrum of G{Kn}, where G is a connected distance regular graph.
Keywords: Cluster | Corona | Distance spectrum
Publisher: Elsevier
Project: University Grant Commission of Government of India, Grant No. MRP(S)-399/08-09/KLMG019/UGC-SWRO

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