A-polynomial for some family of caveman graphs

Abstract

The caveman graph is a graph formed by modifying a set of isolated k-cliques (or caves) by removing one edge from each clique and using it to connect to a neighboring clique along a central cycle such that all n cliques form a single unbroken loop. Caveman graph containing n-copies of k-cliques is denoted as, (n,k)-caveman graph. For a graph G, the A-matrix is defined as, A(G)=[a_ij] in which a_ij=1 if vertices v_i and v_j are adjacent; and 0 otherwise. The polynomial associated with A-matrix is the A-polynomial. In this work, we study A-polynomial for some family of caveman graphs.