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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]
Copyright of IAENG International Journal of Applied Mathematics is the property of International Association of Engineers (IAENG) and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Comparative Analysis of Power Dominator and Power Dominator Equitable Coloring for Specific Tree Structures.
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  Data: <searchLink fieldCode="AR" term="%22Navamani%2C+G%2E%22">Navamani, G.</searchLink><relatesTo>1</relatesTo><i> g_navamani@yahoo.co.in</i><br /><searchLink fieldCode="AR" term="%22Jacquline%2C+L%2E%22">Jacquline, L.</searchLink><relatesTo>2</relatesTo><i> jackinfanci@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Sumathi%2C+V%2E%22">Sumathi, V.</searchLink><relatesTo>3</relatesTo><i> sumathi.math@sairam.edu.in</i><br /><searchLink fieldCode="AR" term="%22Bala%2C+Jyothi%22">Bala, Jyothi</searchLink><relatesTo>4</relatesTo><i> jothibala.snh@rmd.ac.in</i>
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  Data: <searchLink fieldCode="JN" term="%22IAENG+International+Journal+of+Applied+Mathematics%22">IAENG International Journal of Applied Mathematics</searchLink>. Mar2026, Vol. 56 Issue 3, p988-993. 6p.
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  Data: <searchLink fieldCode="DE" term="%22Graph+coloring%22">Graph coloring</searchLink><br /><searchLink fieldCode="DE" term="%22Tree+graphs%22">Tree graphs</searchLink><br /><searchLink fieldCode="DE" term="%22Wireless+sensor+networks%22">Wireless sensor networks</searchLink><br /><searchLink fieldCode="DE" term="%22Resource+allocation%22">Resource allocation</searchLink><br /><searchLink fieldCode="DE" term="%22Telecommunication%22">Telecommunication</searchLink><br /><searchLink fieldCode="DE" term="%22Graph+theory%22">Graph theory</searchLink>
– Name: Abstract
  Label: Abstract
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  Data: 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]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of IAENG International Journal of Applied Mathematics is the property of International Association of Engineers (IAENG) and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Text: English
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        Type: general
      – SubjectFull: Tree graphs
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      – SubjectFull: Wireless sensor networks
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      – SubjectFull: Resource allocation
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              Text: Mar2026
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