7,628 research outputs found

    Connected End Anti-Fuzzy Equitable Dominating Set In Anti-Fuzzy Graphs

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    In this paper, the notion of connected end anti-fuzzy equitable dominating set of an anti-fuzzy graph is discussed. The connected end anti-fuzzy equitable domination number for some standard graphs are obtained. The relation between anti-fuzzy equitable domination number, end anti-fuzzy equitable domination number and connected end anti-fuzzy equitable domination number are established. Theorems related to these parameters are stated and proved

    Equitable eccentric domination in graphs

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    In this paper, we define equitable eccentric domination in graphs. An eccentric dominating set S ⊆ V (G) of a graph G(V, E) is called an equitable eccentric dominating set if for every v ∈ V − S there exist at least one vertex u ∈ V such that |d(v) − d(u)| ≤ 1 where vu ∈ E(G). We find equitable eccentric domination number γeqed(G) for most popular known graphs. Theorems related to γeqed(G) have been stated and proved

    EQUITABLE DOMINATION IN FUZZY GRAPHS

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    Equitable total domination in graphs

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    A subset ‫ܦ‬ of a vertex set ܸሺ‫ܩ‬ሻ of a graph ‫ܩ‬ ൌ ሺܸ, ‫ܧ‬ሻ is called an equitable dominating set if for every vertex ‫ݒ‬ ‫א‬ ܸ െ ‫ܦ‬ there exists a vertex ‫ݑ‬ ‫א‬ ‫ܦ‬ such that ‫ݒݑ‬ ‫א‬ ‫ܧ‬ሺ‫ܩ‬ሻ and |݀݁݃ሺ‫ݑ‬ሻ െ ݀݁݃ሺ‫ݒ‬ሻ| 1, where ݀݁݃ሺ‫ݑ‬ሻ and ݀݁݃ሺ‫ݒ‬ሻ are denoted as the degree of a vertex ‫ݑ‬ and ‫ݒ‬ respectively. The equitable domination number of a graph ߛ ሺ‫ܩ‬ሻ of ‫ܩ‬ is the minimum cardinality of an equitable dominating set of ‫.ܩ‬ An equitable dominating set ‫ܦ‬ is said to be an equitable total dominating set if the induced subgraph ‫ۄܦۃ‬ has no isolated vertices. The equitable total domination number ߛ ௧ ሺ‫ܩ‬ሻ of ‫ܩ‬ is the minimum cardinality of an equitable total dominating set of ‫.ܩ‬ In this paper, we initiate a study on new domination parameter equitable total domination number of a graph, characterization is given for equitable total dominating set is minimal and also discussed Northaus-Gaddum type results
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