Automorphism groups of the constituent graphs of integral distance graphs

Abstract

AbstractIn this paper, we consider the automorphism groups of Cayley graphs which are a basis of a complete Boolean algebra of strongly regular graphs, one of such graph is the integral distance graph [Formula: see text] The automorphism groups of the integral distance graphs Γ were determined by Kovács and Ruff in 2014 and by Kurz in 2009. Our point of interest will be restricted to the one determined by Kovács and Ruff. Here we consider the automorphism groups of subgraphs [Formula: see text] and [Formula: see text] which inherit the properties of [Formula: see text] It will be shown that [Formula: see text] is isomorphic to [Formula: see text] and that [Formula: see text] is isomorphic to [Formula: see text]

Keywords

• Automorphism groups
• integral distance graphs
• Boolean algebra of Cayley sets