On δ(k)-coloring of generalized Petersen graphs

Ellumkalayil, Merlin Thomas; Naduvath, Sudev

doi:10.1142/s1793830921500968

Cited by 2 publications

(1 citation statement)

References 4 publications

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“…The number of bad edges resulting from a near-proper coloring of G is denoted by b k (G). Certain results on this direction can be viewed in [1][2][3][4]9]. In light of these studies, the idea of equitable near-proper coloring of graphs are introduced in [7] and as follows.…”

Section: Introductionmentioning

confidence: 99%

On equitable near-proper coloring of some derived graph classes

Jose

Naduvath

2022

Carpathian Math. Publ.

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An equitable near-proper coloring of a graph $G$ is a defective coloring in which the number of vertices in any two color classes differ by at most one and the bad edges obtained is minimised by restricting the number of color classes that can have adjacency among their own elements. This paper investigates the equitable near-proper coloring of some derived graph classes like Mycielski graphs, splitting graphs and shadow graphs.

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Section: Introductionmentioning

confidence: 99%

On equitable near-proper coloring of some derived graph classes

Jose

Naduvath

2022

Carpathian Math. Publ.

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Some New Results on δ(k)-Coloring of Graphs

Ellumkalayil

Samuel²,

Naduvath

2023

J. Inter. Net.

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Let [Formula: see text] be the minimum number of distinct resources or equipment such as channels, transmitters, antennas and surveillance equipment required for a system’s stability. These resources are placed on a system. The system is stable only if the resources of the same type are placed far away from each other or, in other words, they are not adjacent to each other. Let these distinct resources represent different colors assigned on the vertices of a graph [Formula: see text]. Suppose the available resources, denoted by [Formula: see text], are less than [Formula: see text]. In that case, placing [Formula: see text] resources on the vertices of [Formula: see text] will make at least one equipment of the same type adjacent to each other, which thereby make the system unstable. In [Formula: see text]-coloring, the adjacency between the resources of a single resource type is tolerated. The remaining resources are placed on the vertices so that no two resources of the same type are adjacent to each other. In this paper, we discuss some general results on the [Formula: see text]-coloring and the number of bad edges obtained from the same for a graph [Formula: see text]. Also, we determine the minimum number of bad edges obtained from [Formula: see text]-coloring of few derived graph of graphs. The number of bad edges which result from a [Formula: see text]-coloring of [Formula: see text] is denoted by [Formula: see text].

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On δ(k)-coloring of generalized Petersen graphs

Cited by 2 publications

References 4 publications

On equitable near-proper coloring of some derived graph classes

On equitable near-proper coloring of some derived graph classes

Some New Results on δ(k)-Coloring of Graphs

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