Two-disjoint-cycle-cover vertex pancyclicity of augmented cubes

Abstract

A graph G is two-disjoint-cycle-cover vertex [r1,r2]-pancyclic if, for any two distinct vertices u,v∈V(G) and any positive integers r1≤l≤r2, there are two vertex-disjoint cycles C1 and C2 in G such that C1 contains u with |V(C1)|=l and C2 contains v with |V(C2)|=|V(G)|−l, as well as two vertex-disjoint cycles C1′ and C2′ such that C1′ contains u with |V(C1′)|=|V(G)|−l and C2′ contains v with |V(C2′)|=l. In this study, we investigate the two-disjoint-cycle-cover vertex pancyclicity of augmented cubes and show that the n-dimensional augmented cube AQn is two-disjoint-cycle-cover vertex [3,2n−1]-pancyclic for n≥3.