Some results on Steiner decomposition number of graphs.

Let S be a connected graph with Steiner number S(S). A decomposition S = {S!, S", …, S#} is said to be a Steiner decomposition if S(G) = S(Gi) for all S (1 ≤ i ≤ n). The maximum cardinality obtained for the Steiner decomposition S of S is called the Steiner decomposition number of S and is denoted by S(G). In this paper we present a relation between Steiner decomposition number and independence number of S. Steiner decomposition number for some power of paths are discussed. It is also shown that given any pair S, S of positive integers with S ≥ 2 there exists a connected graph S such that G(S) = m and Sst (G) = n. [ABSTRACT FROM AUTHOR]