Himpunan Kritis pada Graf Bintang

Abstract

Labeling is a one-to-one mapping that maps each element of a graph to Positive numbers called labels. One of its kind is edge-magic total labeling. Under special conditions, the results set of labeled graphs whose subsets are labeled and positioned, which builds the same graph as the labeling, is called the critical set. To obtain the critical set of a graph we must know the type of graph. In this study is a star graph. This study aims to determine the critical set in star graphs. The star graph used is the K1.5 star graph using center points 1, n + 1 and 2n + 1. The research results show that by labeling the total magic side of the K1.5 star graph with center point λ(c) = 1, the magic number k=14 is obtained. The possible critical set of K1.5 graphs is 120. In the K1.5 Star Graph with center point λ(c) = n+ 1, the magic number k=18 is obtained. The possible critical set of K1.5 graphs is 120. In the K1.5 Star Graph with center point λ(c) = 2n + 1, the magic number k=22 is obtained. The possible critical set of K1.5 graphs is 120.