Summary: A labeling of a graph is a mapping of graphs (vertices or edges) into a set of positive integers or a set of non-negative integers. Let \(H\) be a connected, simple, nontrivial, and undirected graph with the vertex set \(V(H)\) and the edge set \(E(H)\). A total \(k\)-labeling is a function \(f_e\) from \(E(H)\) to first natural number \(k_e\) and a function \(f_v\) from \(V(H)\) to non negative even number up to \(2k_v\), where \(k = \max \{k_e, 2k_v\}\). A vertex irregular reflexive \(k\)-labeling of the graph \(G\) is total \(k\)-labeling, if for every two different vertices have different weight, where the weight of a vertex is the sum of labels of edges which are incident this vertex and the vertex label itself. The reflexive vertex strength of the graph \(G\), denoted by \(rvs(G)\) is a minimum \(k\) such that graph \(G\) has a vertex irregular reflexive \(k\)-labelling. In this paper, We will determine the exact value of reflexive vertex strength on ladder graph and bipartite complete \((K_{2,n})\).