On The Edge Irregular Reflexive k-Labeling of Some Cartesian Product Graphs
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Abstract
Let G be a connected and simple graph with vertex set V(G) and edge set E(G). For a graph G, we define k-labeling such that the edges of G are labeled with integers {1,2,3,....,k_e} and the vertices of G are labeled with even integers {0,2,4,....,2k_v}, where k=max{k_e, 2k_v}. If there is a different weight for all edges, then the labeling is called edge irregular reflexive k-labeling. The weight of edge xy, notated by wt(xy) is defined as a sum of label of x, label of xy, and label of y. The minimum k for which G has an edge irregular reflexive k-labeling is defined as reflexive edge strength of G, symbolized by res(G). In this research, we determined the reflexive edge strength of several Cartesian graphs, namely P_5xP_n, S_4xP_n, C_5xC_n, and F_3xP_n.
Keywords: Edge irregular reflexive k-labeling, reflexive edge strength, Cartesian graph.
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