On the spanning trees of finite graphs

Counting the number of spanning trees of graphs

A spanning tree of graph G is a spanning subgraph of G that is a tree. In this paper, we focus our attention on (n,m) graphs, where m = n, n + 1, n + 2, n+3 and n + 4. We also determine some coefficients of the Laplacian characteristic polynomial of fullerene graphs.

NUMBER OF SPANNING TREES FOR DIFFERENT PRODUCT GRAPHS

In this paper simple formulae are derived for calculating the number of spanning trees of different product graphs. The products considered in here consists of Cartesian, strong Cartesian, direct, Lexicographic and double graph. For this purpose, the Laplacian matrices of these product graphs are used. Form some of these products simple formulae are derived and whenever direct formulation was n...

counting the number of spanning trees of graphs

a spanning tree of graph g is a spanning subgraph of g that is a tree. in this paper, we focusour attention on (n,m) graphs, where m = n, n + 1, n + 2 and n + 3. we also determine somecoefficients of the laplacian characteristic polynomial of fullerene graphs.

On the Spanning Trees of Weighted Graphs

Given a weighted graph, let W 1 ; W 2 ; W 3 ; : : : denote the increasing sequence of all possible distinct spanning tree weights. Settling a conjecture due to Kano, we prove that every spanning tree of weight W 1 is at most k ? 1 edge swaps away from some spanning tree of weight W k. Three other conjectures posed by Kano are proven for two special classes of graphs. Finally, we consider the al...

On Spanning Trees of Certain Graphs