Complexity of graphs generated by wheel graph and their asymptotic limits

The literature is very rich with works deal with the enumerating the spanning trees in any graph G since the pioneer Kirchhoff (1847). Generally, the number of spanning trees in a graph can be acquired by directly calculating an associated determinant corresponding to the graph. However, for a large graph, evaluating the pertinent determinant is ungovernable. In this paper, we introduce a new technique for calculating the number of spanning trees which avoids the strenuous computation of the determinant for calculating the number of spanning trees. Using this technique, we can obtain the number of spanning trees of any graph generated by the wheel graph. Finally, we give the numerical result of asymptotic growth constant of the spanning trees of studied graphs.