Nilai Kekuatan Sisi Refleksif pada Graf Ular

Abstract

Let G=(V,E) is a graph. Edge irregular reflexive labeling is defined as edge labels with a positive integer {1,2,…,k_e } and vertices labels with an even positive integer {0,2,…,k_v } such that each edge has a different weight. The minimum value k with k=max⁡{k_e,k_v} of the largest label on a graph G that can be labeled with edge irregular reflexive labeling is the reflexive edge strength of a graph G notated with res(G). This research discusses about edge irregular reflexive labeling of snake graphs are (C_4,2^m),(C_5,2^m), dan (C_6,3^m) with m≥2. A snake graph notated with C_(n,q)^m is defined as graph obtined from m-circle graphs C_n and has a communion points between circle graph i-th and i+1-th. These communion points are called vertebrae points. Which are denoted with u_i for every 1≤i≤m. While q in snake graph notation is the length of the path between u_(i-1) with u_i. The methods used in this research are axiomatic descriptive and pattern detection. The axiomatic descriptive method is a method that is carried out using several definitions and lemma on edge irregular reflexive labeling. The pattern detection method is a method used to formulate patterns so that reflexive edge strength values on snake graphs is obtained. The result of this research was to determine the value of reflexive edge strength and prove that the weight of each edge on the snake graph is different.