Detour Dominating Sets in Cartesian Product of Three Graphs

Author(s): Y Sherlin Nisha, V Rajeswari and Y. Merlin Nisha

Abstract:

A dominating set for a graph G is a subset S of V (G) such that every vertex not in S is adjacent in S is at least any one vertex of S. In this paper presented the detour domination in Cartesian product of three graphs. In the Cartesian product of three graphs, we examine detour dominating sets, which are represented as G×H×K. We investigate the structural characteristics of these products and determine precise values and constraints for the detour domination number in a number of graph classes, such as paths, cycles, and complete graphs. Additionally, we look at how the detour domination number of the product graph is affected by the distinct characteristics of G×H×K. Our findings provide insights into how dominance parameters behave in more intricate graph structures, expanding on previous research on detour domination for single and double Cartesian products.

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Pages: 130-132     |    2 View     |    0 Download