The Complexity of Wheel Graphs with Multiple Edges and Vertices
Yuxuan Wei *
School of Mathematical Sciences, Jiangsu University, Zhenjiang, Jiangsu, 212013, P. R. China.
Zhinan Gao
School of Mathematical Sciences, Jiangsu University, Zhenjiang, Jiangsu, 212013, P. R. China.
Xingyan Lu
School of Mathematical Sciences, Jiangsu University, Zhenjiang, Jiangsu, 212013, P. R. China.
*Author to whom correspondence should be addressed.
Abstract
In this paper, we focus on calculate the number of spanning trees of the general wheel graphs, which means the original wheel graphs adding large amount of vertices and edges. Particularly, we introduce the C-graph and deduce a new equation that computing the spanning trees by removing C-graphs instead of edges. In Addition, we test our results by Kirchhoff’s matrix-tree theorem in some simple cases and provide the tree entropy of the general wheel graphs. Finally, we analyse the relation between the wheel graph and double-wheel graphs and propose the idea of calculating the spanning trees of double-wheel graphs.
Keywords: The number of spanning trees, wheel graph, iterate relations, tree entropy, double-wheel graphs, complex network