A note on dominator chromatic number of line graph and jump graph of some graphs

Kalaivani, R.; Vijayalakshmi, D.

doi:10.31801/cfsuasmas.529578

Cited by 2 publications

(1 citation statement)

References 6 publications

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“…Arumugam et al showed that the dominator coloring problem is NP-hard on bipartite, planar and split graphs [2]. More results on this coloring could be found in [3,21,25,26] and elsewhere.…”

Section: Introductionmentioning

confidence: 99%

Double total dominator chromatic number of graphs

Beggas¹,

Kheddouci²,

Marweni³

2021

Discuss. Math. Graph Theory

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In this paper, we introduce and study a new coloring problem of graphs called the double total dominator coloring. A double total dominator coloring of a graph G with minimum degree at least 2 is a proper vertex coloring of G such that each vertex has to dominate at least two color classes. The minimum number of colors among all double total dominator coloring of G is called the double total dominator chromatic number, denoted by χ t dd (G). Therefore, we establish the close relationship between the double total dominator chromatic number χ t dd (G) and the double total domination number γ ×2,t (G). We prove the NP-completeness of the problem. We also examine the effects on χ t dd (G) when G is modified by some operations. Finally, we discuss the χ t dd (G) number of square of trees by giving some bounds.

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“…Arumugam et al showed that the dominator coloring problem is NP-hard on bipartite, planar and split graphs [2]. More results on this coloring could be found in [3,21,25,26] and elsewhere.…”

Section: Introductionmentioning

confidence: 99%

Double total dominator chromatic number of graphs

Beggas¹,

Kheddouci²,

Marweni³

2021

Discuss. Math. Graph Theory

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On the double total dominator chromatic number of graphs

Beggas¹,

Kheddouci

Marweni

2021

Discrete Math. Algorithm. Appl.

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In this paper, we introduce and study a new coloring problem of graphs called the double total dominator coloring. A double total dominator coloring of a graph [Formula: see text] with minimum degree at least 2 is a proper vertex coloring of [Formula: see text] such that each vertex has to dominate at least two color classes. The minimum number of colors among all double total dominator coloring of [Formula: see text] is called the double total dominator chromatic number, denoted by [Formula: see text]. Therefore, we establish the close relationship between the double total dominator chromatic number [Formula: see text] and the double total domination number [Formula: see text]. We prove the NP-completeness of the problem. We also examine the effects on [Formula: see text] when [Formula: see text] is modified by some operations. Finally, we discuss the [Formula: see text] number of square of trees by giving some bounds.

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A note on dominator chromatic number of line graph and jump graph of some graphs

Cited by 2 publications

References 6 publications

Double total dominator chromatic number of graphs

Double total dominator chromatic number of graphs

On the double total dominator chromatic number of graphs

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