Split Liar Domination on Intuitionistic Fuzzy Graphs

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S. Roseline Mary, L. Selvam


A set S is said to be a liar dominating set if it can identify the location node x of an intruder when any one of the nodes which is closed neighborhood of x lie or wrongly identify the intruder’s location. In other words, Let G = (V,E,µ) be a fuzzy graph. A set S is called a liar dominating set of a fuzzy graph G if it satisfies the following two constraints.

  1. Each node of V (G) is dominated by at least two nodes of V (G)

  2. Each pair of nodes of V (G) is dominated by at least three nodes of V (G)

Liar dominating set lies between double dominating set and triple dominating set since triple dominating set persists a liar dominating set and every liar dominating set double dominates. In this paper, we introduce the split liar dominating set for intuitionistic fuzzy graphs and also discuss some theorems and results with suitable examples.


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