Affiliation:
1. Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA (Segamat Campus), Johor 85000, Malaysia
2. Department of Mathematics, Yazd University, Yazd 89195-741, Iran
Abstract
Let [Formula: see text] be a graph of order [Formula: see text]. A subset [Formula: see text] of [Formula: see text] is a dominating set of [Formula: see text] if every vertex in [Formula: see text] is adjacent to at least one vertex of [Formula: see text]. The domination polynomial of [Formula: see text] is the polynomial [Formula: see text], where [Formula: see text] is the number of dominating sets of [Formula: see text] of size [Formula: see text], and [Formula: see text] is the size of a smallest dominating set of [Formula: see text], called the domination number of [Formula: see text]. Motivated by a conjecture in [S. Alikhani and Y. H. Peng, Introduction to domination polynomial of a graph, ARS Combin. 114 (2014) 257–266] which states that the domination polynomial of any graph is unimodal, we obtain sufficient conditions for this conjecture to hold. Also we study the unimodality of graph [Formula: see text] with [Formula: see text], where [Formula: see text] is an integer.
Publisher
World Scientific Pub Co Pte Lt
Subject
Discrete Mathematics and Combinatorics
Cited by
3 articles.
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