The line graph of the crown graph is distance integral

2021/08/10 by Mirafzal, S. Morteza · 2 citations
#05C50 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2108.05223

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. A 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). In this paper, by using the orbit partition method in algebraic graph theory, we determine the set of all distance eigenvalues of L(Cr(n)) and show that this graph is distance integral.

Cited by

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

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