SECURE DOMINATION IN TRANSFORMATION GRAPH Gxy+

Title

SECURE DOMINATION IN TRANSFORMATION GRAPH Gxy+

Creator

Theresa S.; Kureethara J.V.

Description

In this paper, we characterize graphs for which the secure domination number of the transformation graph Gxy+ is 1 or 2. Also we prove that for any connected graph G with at least 4 pendant vertices, the secure domination number is greater than or equal to the secure domination number of the transformation graph G-++. We also find a bound for the secure domination number of G-+ when G is a tree. 2024 Jangjeon Research Institute for Mathematical Sciences and Physics. All rights reserved.

Source

Proceedings of the Jangjeon Mathematical Society, Vol-27, No. 4, pp. 837-848.

Date

2024-01-01

Publisher

Jangjeon Research Institute for Mathematical Sciences and Physics

Subject

Domination; line graph; secure domination; transformation graph

Coverage

Theresa S., Department of Mathematics, Christ University, Bangalore, India; Kureethara J.V., Department of Mathematics, Christ University, Bangalore, India

Rights

Restricted Access

Relation

ISSN: 15987264

Format

Online

Language

English

Type

Article

Identifier

https://doi.org/10.17777/pjms2024.27.4.837

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