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Comparative Analysis of Power Dominator and Power Dominator Equitable Coloring for Specific Tree Structures.

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Title: Comparative Analysis of Power Dominator and Power Dominator Equitable Coloring for Specific Tree Structures.
Authors: Navamani, G.1 g_navamani@yahoo.co.in, Jacquline, L.2 jackinfanci@gmail.com, Sumathi, V.3 sumathi.math@sairam.edu.in, Bala, Jyothi4 jothibala.snh@rmd.ac.in
Source: IAENG International Journal of Applied Mathematics. Mar2026, Vol. 56 Issue 3, p988-993. 6p.
Subjects: Graph coloring, Tree graphs, Wireless sensor networks, Resource allocation, Telecommunication, Graph theory
Abstract: A power dominator coloring of a graph G is a proper coloring in which each vertex in V (G) power dominates every vertex within at least one color class. The corresponding minimum number of colors is called power dominator chromatic number of G, denoted by Χpd (G). A proper coloring of a graph G is said to be equitably k-colorable if the cardinalities of any two color classes C¹; C², ..., Ck of G differ by at most one; i.e.,||Ci|-|Cj|| ≤ 1: ∀ i, j. The minimum such k is called the equitable chromatic number, denoted by Χe (G). The power dominator equitable coloring of a graph G is a proper equitable κ-coloring if each vertex of V (G) power dominates all vertices of at least one color class satisfying ||Ci|| - ||Cj|| ≤ 1: ∀ i, j. In this paper, we investigate this new parameter and determine the power dominator equitable chromatic number Χpde for certain classes of trees. Power dominator equitable coloring finds diverse applications in computer science and networks, including wireless sensor networks, telecommunication networks, social networks and resource allocation in distributed systems. [ABSTRACT FROM AUTHOR]
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Abstract:A power dominator coloring of a graph G is a proper coloring in which each vertex in V (G) power dominates every vertex within at least one color class. The corresponding minimum number of colors is called power dominator chromatic number of G, denoted by Χpd (G). A proper coloring of a graph G is said to be equitably k-colorable if the cardinalities of any two color classes C¹; C², ..., Ck of G differ by at most one; i.e.,||Ci|-|Cj|| ≤ 1: ∀ i, j. The minimum such k is called the equitable chromatic number, denoted by Χe (G). The power dominator equitable coloring of a graph G is a proper equitable κ-coloring if each vertex of V (G) power dominates all vertices of at least one color class satisfying ||Ci|| - ||Cj|| ≤ 1: ∀ i, j. In this paper, we investigate this new parameter and determine the power dominator equitable chromatic number Χpde for certain classes of trees. Power dominator equitable coloring finds diverse applications in computer science and networks, including wireless sensor networks, telecommunication networks, social networks and resource allocation in distributed systems. [ABSTRACT FROM AUTHOR]
ISSN:19929978