Please use this identifier to cite or link to this item: http://hdl.handle.net/10497/17694
Title: A characterisation of cycle-disjoint graphs with unique minimum weakly connected dominating set
Authors: Koh, Khee Meng
Ting, T. S.
Dong, Fengming
Issue Date: 2012
Citation: Koh, K. M., Ting, T. S., & Dong, F. (2012). A characterisation of cycle-disjoint graphs with unique minimum weakly connected dominating set. Australasian Journal of Combinatorics, 54, 177–187.
Abstract: Let G be a connected graph with vertex set V (G). A set S of vertices in G is called a weakly connected dominating set of G if (i) S is a dominating set of G and (ii) the graph obtained from G by removing all edges joining two vertices in V (G) \ S is connected. A weakly connected dominating set S of G is said to be minimum or a γw-set if |S| is minimum among all weakly connected dominating sets of G. We say that G is γw-unique if it has a unique γw-set. Recently, a constructive characterisation of γw-unique trees was obtained by Lemanska and Raczek [Czechoslovak Math. J. 59 (134) (2009), 95–100]. A graph is said to be cycle-disjoint if no two cycles in G have a vertex in common. In this paper, we extend the above result on trees by establishing a constructive characterisation of γw-unique cycle-disjoint graphs.
URI: http://hdl.handle.net/10497/17694
ISSN: 1034-4942
Website: http://ajc.maths.uq.edu.au/pdf/54/ajc_v54_p177.pdf
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