Some families of graphs with no nonzero real domination roots
Let G be a simple graph of order n . The domination polynomial of G is the polynomial D(G, x) = ∑ni = γ(G)d(G, i)xi , where d(G, i) is the number of dominating sets of G of size i and γ(G) is the domination number of G . A root of D(G, x) is called a domination root of G . Obviously, 0 is a dominati...
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Published in | Electronic journal of graph theory and applications Vol. 6; no. 1; pp. 17 - 28 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Indonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Australia; Institut Teknologi Bandung (ITB), Indonesia
01.01.2018
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Subjects | |
Online Access | Get full text |
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Summary: | Let G be a simple graph of order n . The domination polynomial of G is the polynomial D(G, x) = ∑ni = γ(G)d(G, i)xi , where d(G, i) is the number of dominating sets of G of size i and γ(G) is the domination number of G . A root of D(G, x) is called a domination root of G . Obviously, 0 is a domination root of every graph G with multiplicity γ(G) . In the study of the domination roots of graphs, this naturally raises the question: Which graphs have no nonzero real domination roots? In this paper we present some families of graphs whose have this property. |
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ISSN: | 2338-2287 2338-2287 |
DOI: | 10.5614/ejgta.2018.6.1.2 |