Automorphism group of a family of distance regular graphs which are not distance transitive

2024/03/02 by Das, Angsuman, Mirafzal, S. Morteza
#05C25 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2403.01293

Abstract

Let G_n=ℤ_n× ℤ_n for n≥ 4 and S=\(i,0),(0,i),(i,i): 1≤ i ≤ n-1\⊂ G_n. Define Γ(n) to be the Cayley graph of G_n with respect to the connecting set S. It is known that Γ(n) is a strongly regular graph with the parameters (n²,3n-3,n,6) \cite19. Hence Γ(n) is a distance regular graph. It is known that every distance transitive graph is distance regular, but the converse is not true. In this paper, we study some algebraic properties of the graph Γ(n). Then by determining the automorphism group of this family of graphs, we show that the graphs under study are not distance transitive.

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