Upper domatic number of regular graphs

Libin Chacko Samuel; Mayamma Joseph

doi:10.47443/dml.2021.0054

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Upper domatic number of regular graphs

Author(s)

Libin Chacko Samuel Department of Mathematics, CHRIST (Deemed to be University),Bangalore, Karnataka,India

Mayamma Joseph Department of Mathematics, CHRIST (Deemed to be University),Bangalore, Karnataka,India

Abstract

A partition = fV1; V2; : : : ; Vkg 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 2 . 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.

Publication Details

Page(s) 16-21

DOI 10.47443/dml.2021.0054

Published Journal: Discrete Mathematics Letters, Volume: 8, Issue: 0, Year: 2022

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Keywords

domatic number, r-regular graphs, upper domatic number