Authors

• James Joseph CHRIST (Deemed to be University), India https://orcid.org/0000-0003-4685-4688
• Mayamma Joseph CHRIST (Deemed to be University), India https://orcid.org/0000-0001-5819-247X

DOI: https://doi.org/10.26493/2590-9770.1833.d92 Keywords: Signed graphs, roman dominating function, roman domination number, roman domination edge critical graphs Abstract

A Roman dominating function(RDF) on a signed graph S = (G, σ) 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⁺(v) having f(u) = 2, where f(N[v]) = f(v) + ∑_{u ∈ N(v)} σ(uv)f(u). The weight of an RDF is ω(f) = ∑_v ∈ V f(v) and the minimum weight among all the RDFs on S is called the Roman domination number, γ_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 γ_R(S + uv) < γ_R(S), for any pair of non-adjacent vertices u and v of S, such that the edge uv is positive.