STABILITY OF WEAK ROMAN DOMINATION UPON VERTEX DELETION | Asian Journal of Mathematics and Computer

Allow G=(V, E) to be a graph and f: V0,1,2 to be a function. Where Vi = v|f(v) = i,I = 0,1,2, we write f = (V0, V1, V2). If a vertex inV0 is adjacent to a vertex inV1 V2, it is said to be defended with respect to the function f. With regard to f, a vertex that does not satisfy this criterion is said to be undefended. The function f is said to be a weak Roman dominant function (WRDF) if there exists a vertex u V1 V2 for each vertex u V0, such that no vertex in V is undefended under the new function f′ defined on V by f′ (u) = 1,f′(v) =f(v)1 and f′ (w) = f (w) for all vertices in Vu, v. |V1|+ 2|V2| is the weight of the WRDF f = (V0, V1, V2). The weak Roman dominion number of G is indicated by r and is the lowest weight of a WRDF defined on V. (G). rUVR, which are graphs in which r (Gv) = r (G) for any vertex v V(G), and rCVR, which are graphs in which r (Gv)=r(G) for any v V(G), take importance. We characterise particular graphs for membership in these classes in this study.

Please see the link :- https://www.ikprress.org/index.php/AJOMCOR/article/view/732