Please use this identifier to cite or link to this item: http://scholarbank.nus.edu.sg/handle/10635/102608
Title: A characterisation of cycle-disjoint graphs with unique minimum weakly connected dominating set
Authors: Koh, K.M. 
Ting, T.S.
Dong, F.M.
Issue Date: 2012
Citation: Koh, K.M.,Ting, T.S.,Dong, F.M. (2012). A characterisation of cycle-disjoint graphs with unique minimum weakly connected dominating set. Australasian Journal of Combinatorics 54 (2) : 177-187. ScholarBank@NUS Repository.
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 γ w-set if {pipe}S{pipe} is minimum among all weakly connected dominating sets of G. We say that G is γ w-unique if it has a unique γ w-set. Recently, a constructive characterisation of γ wunique 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 γ w-unique cycle-disjoint graphs.
Source Title: Australasian Journal of Combinatorics
URI: http://scholarbank.nus.edu.sg/handle/10635/102608
ISSN: 10344942
Appears in Collections:Staff Publications

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