Strong weak domination and domination balance in a graph

Sampathkumar, E. and Latha, L. P. (1996) Strong weak domination and domination balance in a graph. Discrete Mathematics, 161 (1-3). pp. 235-242.

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Let G=(V, E) be a graph and u, v is an element of V. Then, u strongly dominates u and v weakly dominates a if(i) uv is an element of E and (ii) deg u greater than or equal to deg v. A set D subset of V is a strong-dominating set (sd-set) of G if every vertex in V-D is strongly dominated by at least one vertex in D. Similarly, a weak-dominating set (wd-set) is defined. The strong (weak) domination number gamma(s) (gamma(w)) of G is the minimum cardinality of an sd-set (wd-set). Besides investigating some relationship of gamma(s) and gamma(w) with other known parameters of G, some bounds are obtained. A graph G is domination balanced if there exists an sd-set D-1 and a wd-set D-2 such that D-1 boolean AND D-2={empty set}. A study of domination balanced graphs is initiated.

Item Type: Article
Subjects: E Mathematical Science > Mathematics
Divisions: Department of > Mathematics
Depositing User: Users 23 not found.
Date Deposited: 24 May 2021 06:52
Last Modified: 04 Feb 2023 06:01

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