EDGE IRREGULAR REFLEXIVE LABELING OF DUMBBELL GRAPH, CORONA OF OPEN LADDER, AND NULL GRAPH

Zalsa, Thetania Miftakul
Indriati, Diari
Martini, Titin Sri

BAREKENG: Jurnal Ilmu Matematika dan Terapan
Vol 18 No 4 (2024): BAREKENG: Journal of Mathematics and Its Application

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 .