The upper domatic number of powers of graphs

Title

The upper domatic number of powers of graphs

Creator

Samuel L.C.; Joseph M.

Description

Let A and B be two disjoint subsets of the vertex set V of a graph G. The set A is said to dominate B, denoted by A ? B, if for every vertex u ? B there exists a vertex v ? A such that uv ? E(G). For any graph G, a partition ? = fV1; V2; : : : ; Vpg of the vertex set V is an upper domatic partition if Vi ? Vj or Vj ? Vi or both for every Vi; Vj ? ?, whenever i ? j. The upper domatic number D(G) is the maximum order of an upper domatic partition. In this paper, we study the upper domatic number of powers of graphs and examine the special case when power is 2. We also show that the upper domatic number of kth power of a graph can be viewed as its k-upper domatic number. 2021 Azarbaijan Shahid Madani University.

Source

Communications in Combinatorics and Optimization, Vol-6, No. 1, pp. 53-65.

Date

2021-01-01

Publisher

Azarbaijan Shahid Madani University

Subject

Domatic number; K-domatic number; K-upper domatic number; Upper do-matic 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.2020.26913.1163

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