EDGE IRREGULAR REFLEXIVE LABELING OF DUMBBELL GRAPH, CORONA OF OPEN LADDER, AND NULL GRAPH - Thetania Miftakul Zalsa; Diari Indriati; Titin Sri Martini (Barekeng)
Graph  is a simple, connected, undirected graph with vertex set  and edge set . A graph  is called to have an edge irregular reflexive -labeling if its vertices can be labeled with even numbers from  until  and its edges can be labeled with positive integers from  to  such that the weights for all the edges are different, where . The weight of edge uv in graph  with  labeling, denoted by , is defined as sum of the edge label and all vertex labels incident to that edge. The reflexive edge strength of a graph , denoted by , is the value of minimum  of the largest label. In this paper, edge irregular reflexive -labeling for Dumbbell Graph  and corona of open ladder and null graph  will be determined. The reflexive edge strength of the Dumbbell Graph  with  and  is  for  and  for  The reflexive edge strength of the corona of open ladder and null graph  with n ≥ 3 and m ≥ 1 is for  and for .