Total Coloring of Certain Classes of Product Graphs

Mohan, S.; Geetha, J.; Somasundaram, K.

doi:10.1016/j.endm.2016.05.016

Cited by 5 publications

(3 citation statements)

References 17 publications

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“…In [9], et al investigated the star edge coloring of the Corona product of Path and some other graphs and discovered the associated chromatic numbers. Then in 2017 [11], total coloring of corona product of two graphs G and H, was studied by Mohan, in which they assumed H as a cycle, a complete graph or a bipartite graph. In 2020, Lu et al [10] investigated the acyclic chromatic numbers that correspond to the corona product of paths or cycles and any simple graph.…”

Section: Introductionmentioning

confidence: 99%

$T$ and $St$-Coloring of Corona Product and Edge Corona Product of Graphs

Moran,

Bora,

Begum

et al. 2023

Int. J. of Appl. Math.

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When coloring a graph's vertices, a particular technique known as T -coloring is used to ensure that the absolute difference between the colors allocated to the end vertices of any edge will not be an element of a predetermined set T of non-negative integers that includes zero. A type of T -coloring of a graph known as ST -coloring is one in which there is a noticeable absolute difference between the assigned colors of each edge's end vertices. Here, we discuss these colorings on the Corona product and the edge corona network of graphs. We obtain a few findings on the chromatic numbers associated with the T and ST -colorings, as well as the span and edge span of these graph products.

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Section: Introductionmentioning

confidence: 99%

$T$ and $St$-Coloring of Corona Product and Edge Corona Product of Graphs

Moran,

Bora,

Begum

et al. 2023

Int. J. of Appl. Math.

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“…Recently [14] it is proved that the graphs K n × K n , C m × C n and G H are type-I graphs, where G is any bipartite graph. Mohan et al [15] proved that certain classes of Corona product graphs are type-I. In [16], they also proved the TCC for certain classes of product graphs.…”

Section: Introductionmentioning

confidence: 99%

“…Mohan et al [15] proved that certain classes of Corona product graphs are type-I. In [16], they also proved the TCC for certain classes of product graphs.…”

Section: Introductionmentioning

confidence: 99%

Total Coloring Conjecture for Certain Classes of Graphs

Vignesh¹,

Geetha²,

Somasundaram³

2018

Algorithms

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A total coloring of a graph G is an assignment of colors to the elements of the graph G such that no two adjacent or incident elements receive the same color. The total chromatic number of a graph G, denoted by χ ′ ′ ( G ) , is the minimum number of colors that suffice in a total coloring. Behzad and Vizing conjectured that for any graph G, Δ ( G ) + 1 ≤ χ ′ ′ ( G ) ≤ Δ ( G ) + 2 , where Δ ( G ) is the maximum degree of G. In this paper, we prove the total coloring conjecture for certain classes of graphs of deleted lexicographic product, line graph and double graph.

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Total colorings of certain classes of lexicographic product graphs

Sandhiya

Geetha

Somasundaram

2021

Discrete Math. Algorithm. Appl.

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A total coloring of a graph G is an assignment of colors to all the elements (vertices and edges) of the graph in such a way that no two adjacent or incident elements receive the same color. The Total Chromatic Number, [Formula: see text] is the minimum number of colors which need to be assigned to obtain a total coloring of the graph [Formula: see text]. The Total Coloring Conjecture made independently by Behzad and Vizing claims that, [Formula: see text], where [Formula: see text] represents the maximum degree of [Formula: see text]. The lower bound is sharp, the upper bound remains to be proved. In this paper, we prove the Total Coloring Conjecture for certain classes of lexicographic product and deleted lexicographic product of graphs.

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Total Coloring of Certain Classes of Product Graphs

Cited by 5 publications

References 17 publications

$T$ and $St$-Coloring of Corona Product and Edge Corona Product of Graphs

$T$ and $St$-Coloring of Corona Product and Edge Corona Product of Graphs

Total Coloring Conjecture for Certain Classes of Graphs

Total colorings of certain classes of lexicographic product graphs

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