Reliability of the Closed-Chain-Fan Social Network

Most researchs about spanning trees are devoted to determine exact formulas for the number of spanning trees in many kinds of special networks, which is an important measure of reliability for a communication network. We consider the closed-chain-fan planar topology Gn, k, as closed chain of n planar fan network Fk having n (k -- 1) nodes, all faces having degree 3 except for the outside and inside ones. Our approach consists on nding a general formula that enumerate spanning trees in the closed-chain-fan planar network Gn, k, depending on n and k to seek the possibilities of interactions between individuals.