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

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)iρi(G)=1∑i≥0(−1)iρi(G)=1, where ρi(G)ρi(G) is the number of ii-regular Hamming subgraphs in a cage-amalgamation graph GG.