Some results on Steiner decomposition number of graphs

Abstract

Let G be a connected graph with Steiner number s(G). A decomposition π = {G1,G2, ...,Gn} is said to be a Steiner decomposition if s(Gi) = s(G) for all i (1 ≤ i ≤ n). The maximum cardinality obtained for the Steiner decomposition π of G is called the Steiner decomposition number of G and is denoted by πst(G). In this paper we present a relation between Steiner decomposition number and independence number of G. Steiner decomposition number for some power of paths are discussed. It is also shown that given any pair m, n of positive integers with m ≥ 2 there exists a connected graph G such that s(G) = m and πst(G) = n.