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Mathematical Based Performance Comparison of TUS and Triple Connected Dominator Coloring Sets for MANET

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R. Jothiraj and B. Chandralekha
» doi: 10.48047/ecb/2023.12.4.217

Abstract

A mobile ad hoc network is a self-created, self-organized and self-administering set of nodes connected via wireless links without the aid of any fixed infrastructure or administrator. The concept of triple umpiring system (TUS) was introduced in [1] by considering the existence of path containing any three vertices (node) of a graph G using triple connected dominator coloring sets. In our system each node’s behavior from source to destination is closely monitored by a set of three umpires. If any misbehavior is noticed umpires flag off the guilty node from the circuit. We have proposed triple connected dominator chromatic number to exemplify the basic TUS for salvaging, the circuit during disruptions in route reply and data forwarding phases. Let G(V,E) be a graph. A triple connected dominator coloring of a graph G is a proper three coloring of G in which every vertex dominates every vertex of atleast one color class. The minimum number of colors required for a triple connected dominator coloring set of G is called the triple connected dominator chromatic number of G and is denoted by (G). tcc  In this paper, we obtain bounds for general graphs and characterize the corresponding extremal graphs.

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