7,628 research outputs found
Connected End Anti-Fuzzy Equitable Dominating Set In Anti-Fuzzy Graphs
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
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 total domination in graphs
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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