New results on upper domatic number of graphs

Title

New results on upper domatic number of graphs

Creator

Samuel L.C.; Joseph M.

Description

For a graph G = (V, E), a partition ? = {V1, V2,..., Vk} of the vertex set V is an upper domatic partition if Vi dominates Vj or Vj dominates Vi or both for every Vi, Vj ? ?, whenever i 6= j. The upper domatic number D(G) is the maximum order of an upper domatic partition of G. We study the properties of upper domatic number and propose an upper bound in terms of clique number. Further, we discuss the upper domatic number of certain graph classes including unicyclic graphs and power graphs of paths and cycles. 2020 Azarbaijan Shahid Madani University

Source

Communications in Combinatorics and Optimization, Vol-5, No. 2, pp. 125-137.

Date

2020-01-01

Publisher

Azarbaijan Shahid Madani University

Subject

Domination; Transitivity; Upper domatic number; Upper domatic partition

Coverage

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

Rights

Restricted Access

Relation

ISSN: 25382128

Format

Online

Language

English

Type

Article

Identifier

https://doi.org/10.22049/CCO.2019.26719.1136

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