Discrepancies of spanning trees and Hamilton cycles

The Numbers of Spanning Trees, Hamilton cycles and Perfect Matchings in a Random Graph

Loop-erased Random Walks, Spanning Trees and Hamiltonian Cycles

We establish a formula for the distribution of loop-erased random walks at certain random times. Several classical results on spanning trees, including Wilson’s algorithm, follow easily, as well as a method to construct random Hamiltonian cycles.

Topological paths, cycles and spanning trees in infinite graphs

We study topological versions of paths, cycles and spanning trees in infinite graphs with ends that allow more comprehensive generalizations of finite results than their standard notions. For some graphs it turns out that best results are obtained not for the standard space consisting of the graph and all its ends, but for one where only its topological ends are added as new points, while rays ...

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...