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A Note on Edge-Domsaturation Number of a Graph
Department of Mathematics, Manonmaniam Sundaranar University, Tirunelveli- 627 012, India
Department of Mathematics, Manonmaniam Sundaranar University, Tirunelveli- 627 012, India
- 1 Department of Mathematics, Manonmaniam Sundaranar University, Tirunelveli- 627 012, India
- 2 Department of Mathematics, Manonmaniam Sundaranar University, Tirunelveli- 627 012, India
Open Journal of Discrete Mathematics·Volume 02 (2012)·Pages 109–113·Published 18 July 2012·DOI10.4236/ojdm.2012.23021
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Abstract
The edge-domsaturation number ds'(G) of a graph G = (V, E) is the least positive integer k such that every edge of G lies in an edge dominating set of cardinality k. In this paper, we characterize unicyclic graphs G with ds'(G) = q – Δ'(G) + 1 and investigate well-edge dominated graphs. We further define γ'–-critical, γ'+-critical, ds'–-critical, ds'+-critical edges and study some of their properties.
KeywordsEdge-Dominating SetEdge-Domination Number<i>ds</i>'- CriticalEdge-Domsaturation NumberWell Edge Dominated Graph
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