Cage-amalgamation graphs, a common generalization of chordal and median graphs

Authors:
Boštjan Brešar;Aleksandra Tepeh Horvat
Affiliations:
FEECS, University of Maribor, Smetanova 17, 2000 Maribor, Slovenia;FEECS, University of Maribor, Smetanova 17, 2000 Maribor, Slovenia
Venue:
European Journal of Combinatorics
Year:
2009

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Abstract

A class of graphs, called cage-amalgamation graphs, that is contained in weakly modular and fiber-complemented graphs and contains median and chordal graphs, is introduced and characterized in several ways. A variation of the Hamming polynomial is also introduced and used in obtaining two tree-like equalities for these graphs, that were previously known for both chordal and median graphs. The first equality is @?"i"="0(-1)^i@r"i(G)=1, where @r"i(G) is the number of i-regular Hamming subgraphs in a cage-amalgamation graph G.