Reciprocal distance spectrum of Indu-Bala product of graphs

Arathy Kalleli Damodaran and Pravas Karuvachery

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creative_2025_34_2_175_188

https://doi.org/10.37193/CMI.2025.02.02

Published on 11 January 2025

Issue no: Vol 34/2025 no. 2 Tags: Indu-Bala product, reciprocal distance equienergetic graphs, reciprocal distance cospectral graphs, Reciprocal distance spectrum

Description

Let $G$ be a simple connected graph. The reciprocal distance spectrum of $G$ is the multiset of reciprocal distance eigenvalues of $G$ . The Indu-Bala product $G \blacktriangledown H$ of two graphs $G$ and $H$ is obtained from two disjoint copies of the join $G \vee H$ of $G$ and $H$ by joining the corresponding vertices in the two copies of $H$ . In this paper we obtain the reciprocal distance spectrum of $G \blacktriangledown H$ in terms of adjacency eigenvalues of $G$ and $H$ . We also construct infinitely many non-isomorphic pairs of reciprocal distance equienergetic graphs and reciprocal distance cospectral graphs of diameter $3$ .