Pushpalatha, L. (1997) The global point-set domination number of a graph. Indian Journal of Pure & Applied Mathematics, 28 (1). pp. 47-51.
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A set D of vertices in a graph G = (V, E) is a dominating set of G if every vertex in V - D is adjacent to some vertex in D. D is a global dominating set if it is a dominating set of both G and its complement (G) over bar. D is a point-set dominating set (psd-set) if for every set S subset of V - D, there exists a vertex v in D such that (S boolean OR {v}) is connected. Further, D is a global psd-set if it is a psd-set of both G and (G) over bar. The point-set domination number gamma(p) of G is the minimum cardinality of a psd-set of G. The global point-set domination number gamma(pg) of G is defined similarly. The following results are obtained for a co-connected graph G of order n: (1) If G has order at least 5, then 3 less than or equal to gamma(pg) less than or equal to n - 2. (2) If G has cut vertices, then gamma(p) less than or equal to gamma(pg) less than or equal to gamma(p) + 1. (3) If G has diameter at least 4, then gamma(p) = gamma(pg).
| Item Type: | Article |
|---|---|
| Subjects: | E Mathematical Science > Mathematics |
| Divisions: | Department of > Mathematics |
| Depositing User: | Users 23 not found. |
| Date Deposited: | 27 May 2021 09:11 |
| Last Modified: | 27 May 2021 09:11 |
| URI: | http://eprints.uni-mysore.ac.in/id/eprint/16645 |
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