On dominator coloring of degree splitting graph of some graphs.

Kalaivani, R.; Vijayalakshmi, D.

doi:10.1088/1742-6596/1139/1/012081

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2021

2023

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“…Merouane et al [32] analyze the dominator chromatic number of different graph families. Vaidya and Shukla [33] have studied the dominator coloring for degree splitting graphs of various graph families. The dominator coloring of some classes of graphs are obtained by Yangyang Zhou et al [34].…”

Section: Introductionmentioning

confidence: 99%

Dominator Coloring of Total Graph of Path and Cycle

Shukla¹,

Chandarana²

2023

Math. models, eng.

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A dominator coloring of a graph G is a proper coloring in which every vertex of G dominates every vertex of at least one-color class possibly its own class and each color class is dominated by at least one vertex. The minimum number of colors required for dominator coloring of G is called the dominator chromatic number of G and is denoted by χd(G). In this paper, we have established the relation between dominator chromatic χd(G), chromatic number χG and domination number γG. We have investigated results on total graphs of path and cycle with χdG = χ G + γ G and χdG = χ G + γ G - 1.

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Section: Introductionmentioning

confidence: 99%