Inverse dominating set in fuzzy graphs
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Let G be a graph with p vertices and let D be a minimum dominating set of G. If V −D contains a dominating set D' of G, then D' is called an inverse dominating set of G with respect to D. The inverse domination number γ(G) of G is the cardinality of a smallest inverse dominating set of G. This concept was introduced and studied by Kulli and Domke in [4] and [2] respectively. In this paper we introduce the concept of inverse dominating set in fuzzy graphs and obtain some bounds for the inverse domination number γ(G). Also we investigate the relationship of γ(G) with the other known parameters. Moreover, we also obtain Nordhaus- Gaddum type results for this parameter.
Abstract
Let G be a graph with p vertices and let D be a minimum dominating set of G. If V −D contains a dominating set D' of G, then D' is called an inverse dominating set of G with respect to D. The inverse domination number γ(G) of G is the cardinality of a smallest inverse dominating set of G. This concept was introduced and studied by Kulli and Domke in [4] and [2] respectively. In this paper we introduce the concept of inverse dominating set in fuzzy graphs and obtain some bounds for the inverse domination number γ(G). Also we investigate the relationship of γ(G) with the other known parameters. Moreover, we also obtain Nordhaus- Gaddum type results for this parameter.
참고문헌 (12)
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