On the independent domination polynomial of a graph

2018/08/21 by Jahari, Somayeh, Alikhani, Saeid · 1 citation
#05C69 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1808.07369

Abstract

An independent dominating set of the simple graph G=(V,E) is a vertex subset that is both dominating and independent in G. The independent domination polynomial of a graph G is the polynomial D_i(G,x)=∑_A x^|A|, summed over all independent dominating subsets A⊆ V. A root of D_i(G,x) is called an independence domination root. We investigate the independent domination polynomials of some generalized compound graphs. As consequences, we construct graphs whose independence domination roots are real. Also, we consider some certain graphs and study the number of their independent dominating sets.

Cited by

• Stability of 2-domination number of a graph

Related

• The Independent Domination Polynomial
• Introduction to Domination Polynomial of a Graph
• Some new results on the total domination polynomial of a graph
• Some new results on domination roots of a graph
• On the roots of total domination polynomial of graphs, II