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• W4381802747 abstract "A dominator coloring of a graph <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mi>G</mml:mi></mml:math> is a proper coloring in which every vertex of <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mi>G</mml:mi></mml:math> 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 <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mi>G</mml:mi></mml:math> is called the dominator chromatic number of <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mi>G</mml:mi></mml:math> and is denoted by <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:msub><mml:mrow><mml:mi>χ</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:msub><mml:mo>(</mml:mo><mml:mi>G</mml:mi><mml:mo>)</mml:mo></mml:math>. In this paper, we have established the relation between dominator chromatic <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:msub><mml:mrow><mml:mi>χ</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:msub><mml:mo>(</mml:mo><mml:mi>G</mml:mi><mml:mo>)</mml:mo></mml:math>, chromatic number <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mi>χ</mml:mi><mml:mfenced separators=|><mml:mrow><mml:mi>G</mml:mi></mml:mrow></mml:mfenced></mml:math> and domination number <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mi>γ</mml:mi><mml:mfenced separators=|><mml:mrow><mml:mi>G</mml:mi></mml:mrow></mml:mfenced></mml:math>. We have investigated results on total graphs of path and cycle with <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:msub><mml:mrow><mml:mi>χ</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:msub><mml:mfenced separators=|><mml:mrow><mml:mi>G</mml:mi></mml:mrow></mml:mfenced><mml:mi mathvariant=normal> </mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant=normal> </mml:mi><mml:mi>χ</mml:mi><mml:mi mathvariant=normal> </mml:mi><mml:mfenced separators=|><mml:mrow><mml:mi>G</mml:mi></mml:mrow></mml:mfenced><mml:mi mathvariant=normal> </mml:mi><mml:mo>+</mml:mo><mml:mi mathvariant=normal> </mml:mi><mml:mi>γ</mml:mi><mml:mi mathvariant=normal> </mml:mi><mml:mfenced separators=|><mml:mrow><mml:mi>G</mml:mi></mml:mrow></mml:mfenced></mml:math> and <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:msub><mml:mrow><mml:mi>χ</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:msub><mml:mfenced separators=|><mml:mrow><mml:mi>G</mml:mi></mml:mrow></mml:mfenced><mml:mi mathvariant=normal> </mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant=normal> </mml:mi><mml:mi>χ</mml:mi><mml:mi mathvariant=normal> </mml:mi><mml:mfenced separators=|><mml:mrow><mml:mi>G</mml:mi></mml:mrow></mml:mfenced><mml:mi mathvariant=normal> </mml:mi><mml:mo>+</mml:mo><mml:mi mathvariant=normal> </mml:mi><mml:mi>γ</mml:mi><mml:mi mathvariant=normal> </mml:mi><mml:mfenced separators=|><mml:mrow><mml:mi>G</mml:mi></mml:mrow></mml:mfenced><mml:mi mathvariant=normal> </mml:mi><mml:mo>-</mml:mo><mml:mi mathvariant=normal> </mml:mi><mml:mn>1</mml:mn></mml:math>." @default.
• W4381802747 created "2023-06-24" @default.
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• W4381802747 date "2023-06-23" @default.
• W4381802747 modified "2023-09-23" @default.
• W4381802747 title "Dominator Coloring of Total Graph of Path and Cycle" @default.
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• W4381802747 doi "https://doi.org/10.21595/mme.2023.23228" @default.
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