Complexity of new families of graphs that have the same average degree and their Entropies

The number of spanning trees is an important quantity characterizing the reliability of a network(graph). Generally, the number of spanning trees in a network can be obtained by directly calculating a related determinant corresponding to the network. However, for a large network, evaluating the relevant determinant is intractable. In this paper, we investigated the number of spanning trees in three sequences of families of graphs of the same average degree 16/3. We used the electrically equivalent transformations and rules of weighted generating function which avoids the laborious computation of the determinant for counting the number of spanning trees. Finally, we determined the entropy of our studied graphs.