On the Higher Order Edge-Connectivity of Complete Multipartite Graphs

Abstract

Let G be a connected graph with p ≥ 2 vertices. For k = 1, 2, ..., P-1, the Kth order edge-connectivity of G, denoted by A(K} (e), is defined to be the smallest number of edges whose removal from e leaves a graph with k + 1 connected components. In this note we determine A(K} (e) for any complete multi partite graph G as a consequence, we give a necessary and sufficient condition for the graph Gn to be factored into spanning trees.