Distance spectrum of Indu–Bala product of graphs

• Main Authors: G. Indulal, R. Balakrishnan
• Format: Article
• Language: English
• Published: Taylor & Francis Group 2016-12-01
• Series: AKCE International Journal of Graphs and Combinatorics
• Subjects: Adjacency spectrum; Distance spectrum; Distance equienergetic graphs; Integral graphs
• Online Access: http://www.sciencedirect.com/science/article/pii/S0972860015300591

The D-eigenvalues μ1,μ2,…,μn of a graph G of order n are the eigenvalues of its distance matrix D and form the distance spectrum or D-spectrum of G denoted by SpecD(G). Let G1 and G2 be two regular graphs. The Indu–Bala product of G1 and G2 is denoted by G1▾G2 and is obtained from two disjoint copies of the join G1∨G2 of G1 and G2 by joining the corresponding vertices in the two copies of G2. In this paper we obtain the distance spectrum of G1▾G2 in terms of the adjacency spectra of G1 and G2. We use this result to obtain a new class of distance equienergetic graphs of diameter 3. We also prove that the class of graphs Kn¯▾Kn+1¯ has integral distance spectrum.