counting the number of spanning trees of 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 Spanning Trees of Threshold Graphs

Cayley’s formula states that there are n spanning trees in the complete graph on n vertices; it has been proved in more than a dozen different ways over its 150 year history. The complete graphs are a special case of threshold graphs, and using Merris’ Theorem and the Matrix Tree Theorem, there is a strikingly simple formula for counting the number of spanning trees in a threshold graph on n ve...

An efficient approach for counting the number of spanning trees in circulant and related graphs

On the Number of Spanning Trees of Graphs

We establish some bounds for the number of spanning trees of connected graphs in terms of the number of vertices (n), the number of edges (m), maximum vertex degree (Δ1), minimum vertex degree (δ), first Zagreb index (M 1), and Randić index (R -1).

On the number of spanning trees of Knm±G graphs

The Kn-complement of a graph G, denoted by Kn − G, is defined as the graph obtained from the complete graph Kn by removing a set of edges that span G; if G has n vertices, then Kn − G coincides with the complement G of the graph G. In this paper we extend the previous notion and derive determinant based formulas for the number of spanning trees of graphs of the form K n ± G, where K m n is the ...