An Improved Upper Bound for Steiner Decomposition Number

Abstract

For a connected graph G with Steiner number s(G), a decomposition \(\pi\) = {G₁, G₂, ..., G_n} is said to be a Steiner decomposition if s(G_i) = s(G) for 1 \(\le\) i \(\le\) n. The maximum cardinality obtained for \(\pi\) is called the Steiner decomposition number and it is denoted as \(\pi\)_st (G)[1]. In this paper, a new parameter for connected graph G denoted by q(G') is introduced. The parameter q(G') denotes the number of edges of G' which is the connected subgraph of G of minimum size having Steiner number same as G. This parameter provides an improved upper bound for the Steiner decomposition number. Here, some properties of graphs based on q(G') and the value of this parameter for the corona product of graphs are presented.