TY - JOUR ID - 14410 TI - Weak Roman domination stable graphs upon edge-addition JO - Communications in Combinatorics and Optimization JA - CCO LA - en SN - 2538-2128 AU - Pushpam, Roushini Leely AU - SRILAKSHMI, NAGARAJAN AD - University of Madras AD - DEPARTMENT OF MATHEMATICS DHANRAJ BAID JAIN COLLEGE Y1 - 2023 PY - 2023 VL - 8 IS - 3 SP - 467 EP - 481 KW - weak Roman domination KW - stability KW - edge addition DO - 10.22049/cco.2022.27765.1348 N2 - A Roman dominating function (RDF) on a graph $G$ is a function $f: V(G) \to \{0, 1, 2\}$ such that every vertex with label 0 has a neighbor with label 2. A vertex $u$ with $f(u)=0$ is said to be undefended if it is not adjacent to a vertex with $f(v)>0$. The function $f:V(G) \to \{0, 1, 2\}$ is a weak Roman dominating function (WRDF) if each vertex $u$ with $f(u) = 0$ is adjacent to a vertex $v$ with $f(v) > 0$ such that the function $f^{\prime}: V(G) \to \{0, 1, 2\}$ defined by $f^{\prime}(u) = 1$, $f^{\prime}(v) = f(v) - 1$ and $f^{\prime}(w) = f(w)$ if $w \in V - \{u, v\}$, has no undefended vertex. A graph $G$ is said to be Roman domination stable upon edge addition, or just $\gamma_R$-EA-stable, if $\gamma_R(G+e)= \gamma_R(G)$ for any edge $e \notin E(G)$. We extend this concept to a weak Roman dominating function as follows: A graph $G$ is said to be weak Roman domination stable upon edge addition, or just $\gamma_r$-EA-stable, if $\gamma_r(G+e)= \gamma_r(G)$ for any edge $e \notin E(G)$. In this paper, we study $\gamma_r$-EA-stable graphs, obtain bounds for  $\gamma_r$-EA-stable graphs and  characterize $\gamma_r$-EA-stable trees which attain the bound.  UR - http://comb-opt.azaruniv.ac.ir/article_14410.html L1 - http://comb-opt.azaruniv.ac.ir/article_14410_5980e502155f4b53abf564175b8a4474.pdf ER -