Huang Qiongxiang

On the number of spanning trees and Eulerian tours in iterated line digraphs

This paper provides closed-form expressions for the number of directed spanning trees and Eulerian tours in iterated line graphs of regular digraphs. Some applications are also considered.Abstract This paper provides closed-form expressions for the number of directed spanning trees and Eulerian tours in iterated line graphs of regular digraphs. Some applications are also considered.

Almost all Cayley graphs are hamiltonian

It has been conjectured that there is a hamiltonian cycle in every finite connected Cayley graph. In spite of the difficulty in proving this conjecture, we show that almost all Cayley graphs are hamiltonian. That is, as the order n of a groupG approaches infinity, the ratio of the number of hamiltonian Cayley graphs ofG to the total number of Cayley graphs ofG approaches 1.

Isomorphisms of circulant diagaphs

LetS⊂Zn−{0}. The circulant digraphDCn(S) is a directed graph with vertex setZn and arc set {(i,i+s): i ∈ Zn, s ∈ S}. A. Adam conjectured thatDCn(S)≅DCn(T) if and only ifT=uS for some unitu modn. In this paper we prove that the conjecture is true ifS is a minimal generating set ofZn and thus determine the full automorphism groups of such digraphs. The methods we employ are new and easy to be understood.

INFINITE CIRCULANTS AND THEIR PROPERTIES

In recent years diverse literatures have been published on circulants (cf. [2] and the references cited therein). In this paper we consider the infinite analogues of circulant and random infinite circulant, and their connectivities and hamiltonian properties are discussed. Especially we answer a question of [4] in the case of infinite (undirected) circulants, and some results on random infinite circulants are also obtained.In recent years diverse literatures have been published on circulants (cf. [2] and the references cited therein). In this paper we consider the infinite analogues of circulant and random infinite circulant, and their connectivities and hamiltonian properties are discussed. Especially we answer a question of [4] in the case of infinite (undirected) circulants, and some results on random infinite circulants are also obtained.

Isomorphisms of circulant digraphs of degree 3

In this paper, we introduce a new approach to characterize the isomorphisms of circulant digraphs. In terms of this method, we completely determine the isomorphic classes of circulant digraphs of degree 3. In particular, we characterize those circulant digraphs of degree 3 which don’t satisfy Ádám’s conjecture.In this paper, we introduce a new approach to characterize the isomorphisms of circulant digraphs. In terms of this method, we completely determine the isomorphic classes of circulant digraphs of degree 3. In particular, we characterize those circulant digraphs of degree 3 which don’t satisfy Adam’s conjecture.