The<i>b</i>-chromatic number of certain graphs and digraphs

Kok, Johan; Naduvath, Sudev

doi:10.1080/09720529.2016.1160512

Cited by 10 publications

(4 citation statements)

References 17 publications

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“…, u k , add the additional edges u i v j , ∀v j ∈ W j . The resultant graph is called a Chithra graph of the given graph G, denoted by C(G) (see [12]). Hence, we have the following theorem.…”

Section: Some New Results On R χ (G)mentioning

confidence: 99%

Rainbow Neighbourhoods of Graphs

Kok,

Sudev,

Jamil

2017

Preprint

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In this paper, we introduce the notion of the rainbow neighbourhood and a related graph parameter namely the rainbow neighbourhood number and report on preliminary results thereof. The closed neighbourhood N [v] of a vertex v ∈ V (G) which contains at least one coloured vertex of each colour in the chromatic colouring of a graph is called a rainbow neighbourhood. The number of rainbow neighbourhoods in a graph G is called the rainbow neighbourhood number of G, denoted by r χ (G). We also introduce the concepts of an expanded line graph of a graph G and a v-clique of v ∈ V (G). With the help of these new concepts, we also establish a necessary and sufficient condition for the existence of a rainbow neighbourhood in the line graph of a graph G.

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Section: Some New Results On R χ (G)mentioning

confidence: 99%

Rainbow Neighbourhoods of Graphs

Kok,

Sudev,

Jamil

2017

Preprint

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“…The family of Chithra graphs has been defined in [4] as follows: Consider the set V(G) of all subsets of the vertex set, V (G). Let W be a collection of any finite number, say k, subsets W i , with repetition of selection allowed.…”

Section: Chithra Graphsmentioning

confidence: 99%

On $J$-Colouring of Chithra Graphs

Kok¹,

Naduvath²

2018

Preprint

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“…Several interesting studies on the b-chromatic numbers and related parameters have been done (see [6,9,10,11,13,14,17,18,19,20]). Motivated by these studies, we extend the concepts of mean and variance of random variables to the b-colouring concepts of graphs as follows.…”

Section: B-chromatic Mean and Variance Of Graphsmentioning

confidence: 99%

Some Results on the $b$-Colouring Parameters of Graphs

Sudev,

Chithra,

Kok

2017

Preprint

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A vertex colouring of a given graph G can be considered as a random experiment. A discrete random variable X, corresponding to this random experiment, can be defined as the colour of a randomly chosen vertex of G and a probability mass function for this random variable can be defined accordingly. In this paper, we study the concepts of mean and variance corresponding to the b-colouring of G and hence determine the values of these parameters for a number of standard graphs.

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Theb-chromatic number of certain graphs and digraphs

Abstract: The b-chromatic number of a graph G is the maximum number k of colours in a proper colouring of G, such that at least one vertex in each colour class has a neighbour in all other classes. In this paper, we discuss the b-chromatic number of certain classes of graphs and digraphs.

Cited by 10 publications

References 17 publications

Rainbow Neighbourhoods of Graphs

Rainbow Neighbourhoods of Graphs

On $J$-Colouring of Chithra Graphs

Some Results on the $b$-Colouring Parameters of Graphs

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