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Discussiones Mathematicae Graph Theory 20(1) (2000) 57-69
DOI: https://doi.org/10.7151/dmgt.1106

MEAN VALUE FOR THE MATCHING AND DOMINATING POLYNOMIAL

Jorge Luis Arocha and Bernardo Llano

Instituto de Matemáticas, UNAM, Circuito Exterior
Ciudad Universitaria, México, D.F. 04510
e-mail: arocha@math.unam.mx
e-mail: bllano@math.unam.mx

Abstract

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.

1991 Mathematics Subject Classification: Primary 05C70, 05A15.

References

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Received 3 February 1999
Revised 6 May 1999