Geodesic
Mean value for the matching and dominating polynomial
Discussiones Mathematicae. Graph Theory, Tome 20 (2000) no. 1, pp. 57-69

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The mean value of the matching polynomial is computed in the family of all labeled graphs with n vertices. We introduce the dominating polynomial of a graph whose coefficients enumerate the dominating sets for a graph and study some properties of the polynomial. The mean value of this polynomial is determined in a certain special family of bipartite digraphs.
Keywords: matching, matching polynomial, dominating set 
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Arocha, Jorge; Llano, Bernardo. Mean value for the matching and dominating polynomial. Discussiones Mathematicae. Graph Theory, Tome 20 (2000) no. 1, pp. 57-69. http://geodesic.mathdoc.fr/item/DMGT_2000_20_1_a3/