The Rupture Degree of Graphs with k-Tree - Open Journal of Discrete Mathematics

OJDM > Vol.6 No.2, April 2016

The Rupture Degree of Graphs with k-Tree ()

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DOI: 10.4236/ojdm.2016.62011 2,430 Downloads 3,304 Views

Author(s)

Yinkui Li^*, Qingning Wang, Xiaoling Wang

Affiliation(s)

College of Mathematics and Statistics, Qinghai Nationalities University, Xining, China.

ABSTRACT

A k-tree of a connected graph G is a spanning tree with maximum degree at most k. The rupture degree for a connected graph G is defined by

, where

and

, respectively, denote the order of the largest component and number of components in

. In this paper, we show that for a connected graph G, if

for any cut-set

, then G has a k-tree.

KEYWORDS

The Rupture Degree, k-Tree, Induced Graph

Share and Cite:

Li, Y. , Wang, Q. and Wang, X. (2016) The Rupture Degree of Graphs with k-Tree. Open Journal of Discrete Mathematics, 6, 105-107. doi: 10.4236/ojdm.2016.62011.

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