The Number Of Spanning Trees In Generalized Complete Multipartite Graphs

Spectral graph theory is mainly about the study on the algebraic properties of adjacency matrix and Laplacian matrix. The spectrum of the adjacency ma-trix research was first used in Quantum chemistry. Research on the spectrum of the Laplacian matrix is earlier than the adjacency matrix of the graph.1847, G.Kirchhoff used the Laplacian matrix spectrum to study the current network and obtained the well-known matrix-tree theorem [21].This article is mainly about how to use the results of matrix-tree theorem to calculate the number of spanning trees of the generalized complete multipartite graph. It is well known in the optimization problem of city construction, such as road construction, we often like to find the not only convenient but also economic transportation routes. Apparently the problem is equivalent to find the minimum spanning tree, so the research of spanning trees is of practical significance.The first chapter mainly introduces the basic knowledge and the main results obtained in this thesis; in the second chapter we first introduces the method of calculating the number of spanning trees of the generalized complete multipartite graphs, and then use this method to find the existing spanning trees number of gen-eralized complete multipartite graph of Fan-Type, after that we obtain the number of spanning trees in generalized complete multipartite graphs of Wheel-Type and Circle-Type; then in the third chapter we begin with a summary of the bounds of the number of spanning trees of the graphs, and then we characterize some bounds on the number of the spanning trees of some generalized complete multipartite graphs.