Graphs of Permutation Groups

Abstract

In this paper we introduce and study permutation graphs of permutation groups. Basic, structural and specific properties of these graphs are investigated and characterized. Further, we obtain formulae for enumerating total number of shortest and longest cycles of permutation graphs.

On Suborbits and Graphs Associated with Action of Alternating Groups on Cartesian Product of Two Sets

“…He defined a suborbital graph Gi corresponding to the suborbital Oi ⊆ X × X as a graph whose vertex set is X and edge set E consists of directed edges from x to y where (x, y) ∈ Oi. Since then, there has been an intensive study on these graphs by several researchers including; [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], among others.…”