A Study on Domination in Signed Graphs

Title

A Study on Domination in Signed Graphs

Creator

Mathias, Anisha Jean

Contributor

Shathish, Sangeetha.

Description

Signed graphs, which represent the positive and negative interactions between networks, have gained signifcant attention in various felds, particularly social network analysis. Domination, a fundamental concept in graph theory, is important in understanding the structural characteristics of graphs and determining the minimum number of vertices needed to cover the entire graph. However, research on domination in the context of signed graphs has been limited, with most studies focusing on graphs. This thesis explores a variant of domination called restrained domination in signed graphs and investigates the characteristic properties of these signed graphs in relation to the restrained domination number. Throughout the thesis, we establish exact values and bounds for the restrained domination number in diferent classes of signed graphs. Additionally, we examine the restrained domination property in various derived signed graphs, including the line signed graph, semi-total point signed graph, semi-total line signed graph, and total signed graph. Additionally, we study criticality concepts associated with the restrained domination number in signed graphs. Specifcally, we analyze the efects of removing edges or vertices from signed graphs, as well as adding edges in signed graphs, on the restrained domination number. Further, we extend the concept of restrained domination number to encompass various variants, namely connected restrained domination number, restrained double domination number, and total restrained domination number for signed graphs. We derive relevant results and newlinefindings for these parameters, contributing to a deeper understanding of domination newlinein signed graphs.

Source

Author's Submission

Date

2023-01-01

Publisher

Christ(Deemed to be University)

Subject

Mathematics and Statistics

Rights

Open Access

Relation

61000285

Format

PDF

Language

English

Type

PhD

Identifier

http://hdl.handle.net/10603/545523