On The Edge Irregular Reflexive k-Labeling of Some Cartesian Product Graphs - Rosita, Merlinda; Marsidi, Marsidi; Sulisawati, Dwi Noviani; Agustin, Ika Hesti (Universitas Dr. Soetomo, 2024)
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=maxk_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.