On the number of independent sets in cycle-separated tricyclic graphs

A cycle-separated tricyclic graph (CSTC graph) is a connected simple graph with nn vertices and n+2n+2 edges whose subgraph induced by its cycles consists of three disjoint cycles. In this paper we investigate the number of independent sets in CSTC graphs. We show that the tight upper bound for the number of independent sets in the nn-vertex CSTC graphs is 48×2n−9+948×2n−9+9 (for n≥9n≥9); we also characterize the extremal graph with respect to the aforementioned bound.