3-Sequent achromatic sum of graphs

Title

3-Sequent achromatic sum of graphs

Creator

Dominic C.; Devassia J.V.

Description

Three vertices x,y,z in a graph G are said to be 3-sequent if xy and yz are adjacent edges in G. A 3-sequent coloring (3s coloring) is a function ?: V (G) ?{1, 2,...,k} such that if x,y and z are 3-sequent vertices, then either ?(x) = ?(y) or ?(y) = ?(z) (or both). The 3-sequent achromatic number of a graph G, denoted ?3s(G), equals the maximum number of colors that can be used in a coloring of the vertices' of G such that if xy and yz are any two sequent edges in G, then either x or z is colored the same as y. The 3-sequent achromatic sum of a graph G, denoted a'3s(G), is the greatest sum of colors among all proper 3s-coloring that requires ?3s(G) colors. This research initiates the study of 3-sequent achromatic sum and finds the exact values of this parameter for some known graphs. Furthermore, we calculate the a'3s(G) of corona product, Cartesian product of the graphs and some important results have been proved and a comparative study is carried out. 2021 World Scientific Publishing Company.

Source

Discrete Mathematics, Algorithms and Applications, Vol-13, No. 4

Date

2021-01-01

Publisher

World Scientific

Subject

3-Sequent vertex coloring; 3-sequent vertex coloring number; 3s achromatic number; 3s achromatic sum

Coverage

Dominic C., Department of Mathematics, Christ (Deemed to Be University), Bangalore, Karnataka, 560029, India; Devassia J.V., Tecnologico de Monterrey, School of Engineering and Sciences, Mexico, Mexico

Rights

Restricted Access

Relation

ISSN: 17938309

Format

Online

Language

English

Type

Article

Identifier

https://doi.org/10.1142/S1793830921500397

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