Independence Numbers in Trees

DOI: 10.4236/ojdm.2015.53003   PDF   HTML   XML   3,939 Downloads   4,724 Views   Citations

Abstract

The independence number of a graph G is the maximum cardinality among all independent sets of G. For any tree T of order n ≥ 2, it is easy to see that . In addition, if there are duplicated leaves in a tree, then these duplicated leaves are all lying in every maximum independent set. In this paper, we will show that if T is a tree of order n ≥ 4 without duplicated leaves, then . Moreover, we constructively characterize the extremal trees T of order n ≥ 4, which are without duplicated leaves, achieving these upper bounds.

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Jou, M. and Lin, J. (2015) Independence Numbers in Trees. Open Journal of Discrete Mathematics, 5, 27-31. doi: 10.4236/ojdm.2015.53003.

Conflicts of Interest

The authors declare no conflicts of interest.

References

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