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THE REFLEXIVE EDGE STRENGTH OF THE PENTAGONAL SNAKE GRAPH AND CORONA OF THE OPEN TRIANGULAR LADDER AND NULL GRAPH Indriati, Diari; Utami, Risma Listya; Utomo, Putranto Hadi
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 18 No 4 (2024): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol18iss4pp2757-2766

Abstract

Assume that be an undirected simple graph with vertex set and edge set . The edge irregular reflexive -labeling of graph is a labeling selects positive integers from 1 to as edge labels and non negative even numbers from 0 to as vertex labels, and the weights assigned to each edge are distinct, where . On graph with labeling, the weight of edge is represented by which is defined as the sum of edge label and all vertex labels incident to that edge. Reflexive edge strength of graph is the minimum of the highest label, denoted by . In this research, reflexive edge strength for pentagonal snake graph and corona of open triangular ladder and null graph will be determined. The method of this research is literature study, the lower bound of determined by Ryan’s lemma and the upper bound by labeling. The reflexive edge strength of pentagonal snake graph with is for and for The reflexive edge strength of corona of open triangular ladder and null graph with n ≥ 3 and m ≥ 1 is and .