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Strong weak domination and domination balance in a graph

Strong weak domination and domination balance in a graph,10.1016/0012-365X(95)00231-K,Discrete Mathematics,E. Sampathkumar,L. Pushpa Latha

Strong weak domination and domination balance in a graph   (Citations: 6)
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Let G = (V, E) be a graph and u, v ~ V. Then, u strongly dominates v and v weakly dominates u if (i) uv ~ E and (ii) deg u >/deg v. A set D c 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 7s (7w) of G is the minimum cardinality of an sd-set (wd-set). Besides investigating some relationship of ?s and ?w with other known parameters of G, some bounds are obtained. A graph G is domination balanced if there exists an sd-set D1 and a wd-set/)2 such that D1 c~D2 = 0. A study of domination balanced graphs is initiated.
Journal: Discrete Mathematics - DM , vol. 161, no. 1-3, pp. 235-242, 1996
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    • ...i) the induced subgraphhSi is connected, then S is a connected dominating set (Sampathkumar and Walikar [14]);...
    • ...iii) for all u2 V S, there exists a vertex v2 S such that uv2 E and deg(v) deg(u), then S is called a strong dominating set, and S is a weak dominating set if, for all u 2 V S, there exists a vertex v 2 S such that uv 2 E and deg(v) deg(u) (Pushpa Latha and Sampathkumar [14])...

    S. Balasubramanianet al. Gallai Theorems Involving Domination Parameters

    • ...The strong domination and independent strong domination numbers were studied in [6, 9, 13, 14, 16]...
    • ...Corollary 1 (Sampathkumar and Pushpa Latha [16]) Any K1;3-free graph is strong domination perfect...
    • ...The weak domination number ∞W(G) is the minimum cardinality of a weak dominating set of G, and the independent weak domination number iW(G) is the minimum cardinality of an independent weak dominating set of G. Other results on these parameters can be found in [7, 8, 9, 15, 16]...
    • ...It was proved in [16] that any K1;3-graph is weak domination perfect...

    Dieter Rautenbachet al. Perfect graphs of strong domination and independent strong domination

    • ...The strong domination and independent strong domination numbers were studied in [6,9,13,14,16]...
    • ...Corollary 1 (Sampathkumar and Pushpa Latha [16])...
    • ...It was proved in [16] that any K1;3-graph is weak domination perfect...

    D. Rautenbachet al. Perfect graphs of strong domination and independent strong domination

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