The total upper domatic number of a graph

Title

The total upper domatic number of a graph

Creator

Samuel L.C.; Joseph M.

Description

Let G = (V, E) be a graph with no isolated vertices. For two disjoint subsets A and B of V , if every vertex in B is adjacent to at least one vertex in A, then the set A is said to dominate set B. A partition ? = {V1, V2, . . ., Vk} of the vertex set V is a total upper domatic partition of G if Vi dominates Vj or Vj dominates Vi or both, for any Vi, Vj ? ? and G[Vi], 1 ? i ? k, has no isolated vertices. The total upper domatic number Dt(G) of G is the maximum order of a total upper domatic partition of G. In this paper, we initiate a study on the concept of total upper domatic number and determine the bounds of Dt(G) and exact values of the same for some classes of graphs. World Scientific Publishing Company.

Source

Asian-European Journal of Mathematics

Date

2025-01-01

Publisher

World Scientific

Subject

Domatic number; total upper domatic number; upper domatic number

Coverage

Samuel L.C., Department of Mathematics, Christ University, India; Joseph M., Department of Mathematics, Christ University, India

Rights

Restricted Access

Relation

ISSN: 17935571

Format

Online

Language

English

Type

Article

Identifier

https://doi.org/10.1142/S1793557124501389

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