Upper domatic number of regular graphs

Title

Upper domatic number of regular graphs

Creator

Samuel L.C.; Joseph M.

Description

A partition ? = {V1, V2, , Vk } of the vertex set V (G) of a graph G = (V, E) is an upper domatic partition if Vi dominates Vj or Vj dominates Vi or both for all Vi, Vj ? ?. The maximum order of an upper domatic partition of G is called the upper domatic number D(G) of G. In this article, we determine the upper domatic number of 4-regular graphs. We also find the upper domatic number of 5-regular graphs with girth at least five and determine the upper domatic number of the complements of cycles. 2021 the authors.

Source

Discrete Mathematics Letters, Vol-8, pp. 16-21.

Date

2022-01-01

Publisher

Shahin Digital Publisher

Subject

domatic number; r-regular graphs; upper domatic number

Coverage

Samuel L.C., Department of Mathematics, CHRIST (Deemed to be University), Karnataka, Bangalore, India; Joseph M., Department of Mathematics, CHRIST (Deemed to be University), Karnataka, Bangalore, India

Rights

All Open Access; Gold Open Access

Relation

ISSN: 26642557

Format

Online

Language

English

Type

Article

Identifier

https://doi.org/10.47443/dml.2021.0054

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