The Super Spanning Connectivity of Arrangement Graphs

Abstract

A k-container C(u, v) of a graph G is a set of k internally disjoint paths between u and v. A k-container C(u, v) of G is a k * -container if it is a spanning subgraph of G. A graph G is k *connected if there exists a k * -container between any two different vertices of G. A k-regular graph G is super spanning connected if G is i * -container for all 1 ≤ i ≤ k. In this paper, we prove that the arrangement graph A n,k is super spanning connected if n ≥ 4 and n − k ≥ 2.