EDGE IRREGULAR REFLEXIVE LABELING ON MONGOLIAN TENT GRAPH (M_(m,3)) AND DOUBLE QUADRILATERAL SNAKE GRAPH

Abstract

Let G be an undirected, connected, and simple graph with edges set E(G)and vertex set V(G). An edge irregular reflexive k-labeling f is one in which the label for each edge is an integer number {1,2,…, k_e} and the label for each vertex is an even integer number {0,2,4,…,2k_v}, k = max{ k_e,2k_v}. This type of labeling results in distinct weights for each edge. The weight of an edge xy in a graph G with labeling f, indicated by wt (xy), is the total of the labels on the vertex that are incident to the edge as well as the edge label. The minimum value k of the largest label in the graph G is referred to as res (G), which stands for the reflexive edge strength of the graph G. The topic of edge irregular reflexive k-labeling for mongolian tent graph (M_(m,n)) and double quadrilateral snake graph (D(Q_n )) will be discussed in this paper. The res (M_(m,n)),m≥2,n=3 has been obtained that is ⌈(5m-1)/3⌉ for 5m-1≢2,3 (mod 6) and ⌈(5m-1)/3⌉+1 for 5m-1≡2,3 (mod 6). Also the res (D(Q_n )),n≥2 has been obtained that is ⌈(7n-7)/3⌉ for 7n-7≢2,3 (mod 6) and ⌈(5m-1)/3⌉+1 for 7n-7≡2,3 (mod 6).