Edge criticality in signed graphs admitting a Roman dominating function

Title

Edge criticality in signed graphs admitting a Roman dominating function

Creator

Joseph, James; Joseph, Mayamma

Description

A Roman dominating function(RDF) on a signed graph S = (G, ?) is a function f: V (S) ? {0, 1, 2} such that f(N[v]) ? 1 for every vertex v ? V (S) and any vertex v with f(v) = 0 has a neighbour u ? N + P (v) having f(u) = 2, where f(N[v]) = f(v) + ?u?N(v) ?(uv)f(u). The weight of an RDF is ?(f) = ?v?V f(v) and the minimum weight among all the RDFs on S is called the Roman domination number, ?R(S). In this article we explore the concept of edge criticality in signed graphs admitting an RDF by examining the signed graphs S such that ?R(S+uv) < ?R(S), for any pair of non-adjacent vertices u and v of S, such that the edge uv is positive. This work is licensed under https://creativecommons.org/licenses/by/4.0/

Source

Art of Discrete and Applied Mathematics;

Date

01-01-2025

Publisher

University of Primorska

Subject

roman dominating function; roman domination edge critical graphs; roman domination number; Signed graphs

Coverage

Joseph J., CHRIST (Deemed to be University), Bangalore, 560029, India; Joseph M., CHRIST (Deemed to be University), Bangalore, 560029, India

Rights

All Open Access; Gold Open Access

Relation

ISSN: 25909770;

Format

online

Language

English

Type

Article

Identifier

https://doi.org/10.26493/2590-9770.1833.d92

https://www.scopus.com/pages/publications/105017653688?origin=resultslist