The Neighborhood Polynomial of Chordal Graphs

We study the neighborhood polynomial and complexity of its computation for chordal graphs. The a graph is generating function subsets vertices that have common neighbor. introduce parameter graphs called anchor width an algorithm to compute which runs in time if polynomially bounded. maximal number different sub-cliques clique appear as neighborhood. Furthermore we some subclasses such comparability with bounded leafage. leafage minimum leaves host tree subtree representation. show at most $n^{\ell}$ where $\ell$ denotes This shows computing possible while it NP-hard general