Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 10 3 2025 09 01 A characterization of locating Roman domination edge critical graphs 531 537 14678 10.22049/cco.2023.29108.1853 EN H. Abdollahzadeh Ahangar Department of Mathematics, Babol Noshirvani University of Technology, Shariati Ave., Babol, I.R. Iran H. Rahbani Department of Mathematics, Babol Noshirvani University of Technology, Shariati Ave., Babol, I.R. Iran M.R. Sadeghi Department of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, I.R. Iran Journal Article 2023 09 30 A Roman dominating function (or just \textit{RDF}) on a graph $G =(V, E)$ is a function $f: V \longrightarrow \{0, 1, 2\}$ satisfying the condition that every vertex $u$ for which $f(u) = 0$ is adjacent to at least one vertex $v$ for which $f(v) = 2$. The weight of an \textit{RDF} $f$ is the value $f(V)=\sum_{u \in {V}}f(u)$. An \textit{RDF} $f$ can be represented as $f=(V_0,V_1,V_2)$, where $V_i=\{v\in V:f(v)=i\}$ for $i=0,1,2$. An \textit{RDF} $f=(V_0,V_1,V_2)$ is called a locating Roman dominating function (or just \textit{L\textit{RDF}}) if $N(u)\cap V_2\neq N(v)\cap V_2$ for any pair $u,v$ of distinct vertices of $V_0$. The locating-Roman domination number $\gamma_R^L(G)$ is the minimum weight of an \textit{L\textit{RDF}} of $G$. A graph $G$ is said to be a locating Roman domination edge  critical graph, or just $\gamma_R^L$-edge critical graph, if $\gamma_R^L(G-e)>\gamma_R^L(G)$ for all $e\in E$. The purpose of this paper is to characterize the class of $\gamma_R^L$-edge critical graphs. https://comb-opt.azaruniv.ac.ir/article_14678_d3430644fcd1f91fa1590ba89f1494de.pdf