Counting graph isomorphisms among chordal graphs with restricted clique number

In this paper, we study the following problem: given two graphs G, H and an isomorphism phi between an induced subgraph of G and an induced subgraph of H, compute the number of isomorphisms between G and H that do not contradict phi. We show that this problem can be solved in 0(((k+1)(k+1)!)(2)n(3)) time when the input graphs are restricted to chordal graphs with clique number at most k+1. To prove this, we first show that the tree model of a chordal graph can be uniquely constructed in 0(n(3)) time except for the ordering of children of each node. Then, we show that the number of phi-isomorphisms between G and H can be efficiently computed by use of the tree model.