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Saeid Alikhani, Yee-hock Peng DOMINATING SETS AND DOMINATION POLYNOMIALS OF CERTAIN GRAPHS, II

2010
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Opuscula Mathematica •
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unpublished

The domination polynomial of a graph G of order n is the polynomial D(G, x) = P n i=γ(G) d(G, i)x i , where d(G, i) is the number of dominating sets of G of size i, and γ(G) is the domination number of G. In this paper, we obtain some properties of the coefficients of D(G, x). Also, by study of the dominating sets and the domination polynomials of specific graphs denoted by G ′ (m), we obtain a relationship between the domination polynomial of graphs containing an induced path of length at

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