# Search results for: Xueliang Li

Graphs and Combinatorics > 2002 > 18 > 1 > 193-200

Discussiones Mathematicae Graph Theory > 2001 > 21 > 2 > 159-166

Discrete Mathematics > 2000 > 223 > 1-3 > 327-336

Graphs and Combinatorics > 2002 > 18 > 1 > 193-200

Abstract.A weighted graph is a graph in which each edge e is assigned a non-negative number w(e), called the weight of e. The weight of a cycle is the sum of the weights of its edges. The weighted degree dw(v) of a vertex v is the sum of the weights of the edges incident with v. In this paper, we prove the following result: Suppose G is a 2-connected weighted graph which satisfies the following conditions:...

Discussiones Mathematicae Graph Theory > 2001 > 21 > 2 > 159-166

A weighted graph is a graph in which each edge e is assigned a non-negative number w(e), called the weight of e. The weight of a cycle is the sum of the weights of its edges. The weighted degree $d^w(v)$ of a vertex v is the sum of the weights of the edges incident with v. In this paper, we prove the following result: Suppose G is a 2-connected weighted graph which satisfies the following conditions:...

Discrete Mathematics > 2000 > 223 > 1-3 > 327-336

A weighted graph is a graph in which each edge is assigned a non-negative number, called the weight. The weight of a path (cycle) is the sum of the weights of its edges. The weighted degree of a vertex is the sum of the weights of the edges incident with the vertex. A usual (unweighted) graph can be considered as a weighted graph with constant weight 1. In this paper, it is proved that for a 2-connected...