The distance spectrum of the line graph of the crown graph

2025/08/10 by Mirafzal, S. Morteza · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.07202

Abstract

The distance eigenvalues of a connected graph G are the eigenvalues of its distance matrix D(G). A graph is called distance integral if all of its distance eigenvalues are integers. Let n ≥ 3 be an integer. The crown graph Cr(n) is a graph obtained from the complete bipartite graph K_n,n by removing a perfect matching. Let L(Cr(n)) denote the line graph of the crown graph Cr(n). Using the equitable partition method, the set of distinct distance eigenvalues of the graph L(Cr(n)) has been determined which shows that this graph is distance integral [S.Morteza Mirafzal, The line graph of the crown graph is distance integral, Linear and Multilinear Algebra 71, no. 4 (2023): 662-672]. The distance spectrum of the graph L(Cr(n)) has not been found yet. In this paper, having the set of distance eigenvalues of L(Cr(n)) in the hand, we determine the distance spectrum of this graph.

Citations

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Cited by

• The distance spectrum of the bipartite double cover of strongly regular graphs

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