On the zeros of domination polynomial of a graph. (English) Zbl 1232.05098
Brualdi, Richard A. (ed.) et al., Combinatorics and graphs. Selected papers based on the presentations at the 20th anniversary conference of IPM on combinatorics, Tehran, Iran, May 15–21, 2009. Dedicated to Reza Khosrovshahi on the occasion of his 70th birthday. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4865-4/pbk). Contemporary Mathematics 531, 109-115 (2010).
Summary: The domination polynomial of a graph of order is the polynomial
where is the number of dominating sets of of size . Every root of is called a domination root of . In this paper, we completely determine the domination roots of all graphs with exactly three distinct domination roots. Also, we show that for every forest , , where is the independence number of .
|05C69||Dominating sets, independent sets, cliques|