Some results on Steiner decomposition number of graphs

Abstract EN

Let � be a connected graph with Steiner number �(�).

A decomposition � = {�!, �", … , �#} is said to be a Steiner decomposition if �(�$) = �(�) for all � (1 ≤ � ≤ �).

The maximum cardinality obtained for the Steiner decomposition � of � is called the Steiner decomposition number of � and is denoted by �%&(�).

In this paper we present a relation between Steiner decomposition number and independence number of �.

Steiner decomposition number for some power of paths are discussed.

It is also shown that given any pair �, � of positive integers with � ≥ 2 there exists a connected graph � such that �(�) = � and �%&(�) = �.