Ideal co-secure domination in graphs

Title

Ideal co-secure domination in graphs

Creator

Theresa S.; Sangeetha V.

Description

A set S ? V of a graph G = (V, E) is a co-secure dominating set if for every u ? S, there exists v ? V \ S such that uv ? E and (S \ {u}) ? {v} is a dominating set of G. The minimum cardinality of a co-secure dominating set of G is the co-secure domination number and is denoted by ?cs(G). In this paper we initiate the evaluation of a domination parameter known as the ideal co-secure domination and is defined as follows: A set D ? V is an ideal co-secure dominating set of a graph G = (V, E) if for every u ? D and for every v ? V \ D such that uv ? E, (D \ {u}) ? {v} is a dominating set of G. The minimum cardinality of an ideal co-secure dominating set of G is the ideal co-secure domination number and is denoted by ?ics(G). We look to determine the ideal co-secure domination number of some families of standard graphs and obtain sharp bounds. We also provide the conditions necessary for the trees to have ideal co-secure domination number equal to n - 2. 2020 Author(s).

Source

AIP Conference Proceedings, Vol-2236

Date

2020-01-01

Publisher

American Institute of Physics Inc.

Coverage

Theresa S., Department of Mathematics, CHRIST (Deemed to Be University), Bengaluru, India; Sangeetha V., Department of Mathematics, CHRIST (Deemed to Be University), Bengaluru, India

Rights

Restricted Access

Relation

ISSN: 0094243X; ISBN: 978-073541995-7

Format

Online

Language

English

Type

Conference paper

Identifier

https://doi.org/10.1063/5.0006826

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