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On the domination subdivision numbers of trees (2010)
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| Venue: | AUSTRALASIAN JOURNAL OF COMBINATORICS VOLUME 46 (2010), PAGES 233–239 |
BibTeX
@MISC{Sharada10onthe,
author = {B. Sharada and et al.},
title = { On the domination subdivision numbers of trees},
year = {2010}
}
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Abstract
A set D of vertices of a graph G is a dominating set if every vertex in V \ D is adjacent to some vertex in D. The domination number γ(G) of G is the minimum cardinality of a dominating set of G. The domination subdivision number of G is the minimum number of edges that must be subdivided (where each edge in G can be subdivided at most once) in order to increase the domination number. Arumugam has shown that for any tree, the domination subdivision number always lies between one and three inclusive. In this paper, we provide a constructive characterization of trees whose domination subdivision number is exactly two.
