Hamming polynomials and their partial derivatives

Authors:
Boštjan Brešar;Paul Dorbec;Sandi Klavar;Michel Mollard
Affiliations:
University of Maribor, Faculty of Electrical Engineering and Computer Science, Smetanova 17, 2000 Maribor, Slovenia;ERTé Maths í Modeler, Groupe de recherche GéoD, Laboratoire Leibniz, 46 av. Félix Viallet, 38031 Grenoble CEDEX, France;Department of Mathematics and Computer Science, PeF, University of Maribor, Koroška cesta 160, 2000 Maribor, Slovenia;ERTé Maths í Modeler, Groupe de recherche GéoD, Laboratoire Leibniz, 46 av. Félix Viallet, 38031 Grenoble CEDEX, France
Venue:
European Journal of Combinatorics
Year:
2007

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Abstract

Hamming graphs are Cartesian products of complete graphs and partial Hamming graphs are their isometric subgraphs. The Hamming polynomial h(G) of a graph G is introduced as the Hamming subgraphs counting polynomial. K"k-derivates @?"kG(k=2) of a partial Hamming graph are also introduced. It is proved that for a partial Hamming graph G, @?h(G)@?x"k=h(@?"kG). A couple of combinatorial identities involving the coefficients of the Hamming polynomials of Hamming graphs are also proven.