Disjoint Steiner Trees in the Balanced Complete Multipartite Networks

Abstract

The generalized k‐connectivity κk(G) of a graph G, introduced by Hager in 1985, is a natural generalization of the concept of connectivity κ(G), which is just for k = 2. In (Basrah Journal of Science, 37(3) (2019), 430–441), authors discussed the problem of internally disjoint Steiner trees in an equally complete k‐partite network G by determining its generalized 3‐connectivity κ3(G). In this paper, we by determining the exact value of the generalized 4, 5‐(edge)‐connectivity of the balanced complete n‐partite graph to investigate the edge disjoint Steiner trees in the balanced complete n‐partite networks.