Kirchhoff's Matrix Tree Theorem permits the calculation of the number of spanning trees in
any given graph G through the evaluation of the determinant of an associated matrix. In the …

In this paper we develop a method for determining the exact number of spanning trees in
(directed or undirected) circulant graphs. Using this method we can, for any class of circulant …

For a graph G, let fij be the number of spanning rooted forests in which vertex j belongs to a
tree rooted at i. In this paper, we show that for a path, the fij's can be expressed as the …

We explicitly compute the effective resistances between any two vertices of a ladder graph
by using circuit reductions. Using our findings, we obtain explicit formulas for Kirchhoff index …

Цель настоящего обзора–изучение инвариантов циклических накрытий графов. При
этом накрываемый граф предполагается фиксированным, а циклическая группа …

This paper offers some probabilistic and combinatorial insights into tree formulas for the
Green function and hitting probabilities of Markov chains on a finite state space. These tree …

In the present paper we give a new method for calculating Jacobian group J ac (GP (n, k)) of
the generalized Petersen graph GP (n, k). We show that the minimum number of generators …

In this paper, we develop a new method to produce explicit formulas for the number τ (n) of
spanning trees in the undirected circulant graphs C n (s 1, s 2,…, sk) and C 2 n (s 1, s 2 …

A multi-fan graph is a graph of the form [Formula: see text], where b is a universal vertex, and
[Formula: see text] is the disjoint union of paths [Formula: see text] for i= 1, 2,…, k. In …

We consider a family of I-graphs I (n, k, l), which is a generalization of the class of
generalized Petersen graphs. In the present paper, we provide a new method for counting …