Counting the Number of Spanning trees in Fan Graphs Families

The number of spanning trees is a parameter of architectural and dynamic proprieties of a graph. Computing spanning trees of a graph is a NP-hard problem in graph theory. Algorithms counting this number could implement universal algebraic methods namely "Matrix tree theorem". However, the higher computational complexity makes these algorithms ineffective in the practical areas for a large network. In this paper, we suggest a combinational method based on separation and contraction techniques, investigating analytic formulas compute the number of spanning trees in the fan graphs families.