Abstract
A nontrivial path is called a branch if it has only internal vertices of degree two and end vertices of degree not two. A set S of branches of a graph G is called a branch cut if the deletion of all edges and internal vertices of branches of S results in more components than G. A minimal branch cut is called a branch-bond. In this paper, we found some relationships amongst branch-bonds, weighted graphs and two-factors in iterated line graphs. We also obtained some bounded number of components in two-factor of iterated line graphs by using the concept of branch-bonds.
Acknowledgements
The authors are indebted to the anonymous referees for their nice suggestion to make the present version more readable. This research is supported by Nature Science Funds of China.