L(2,1) Labeling of Lollipop and Pendulum Graphs
- 10.2991/acsr.k.220202.010How to use a DOI?
- L(2, 1) Labeling; Lollipop graph; Pendulum graph
One of the topics in graph labeling is L(2,1) labeling which is an extension of graph labeling. Definition of L(2,1) labeling is a function that maps the set of vertices in the graph to non-negative integers such that every two vertices u, v that have a distance one must have a label with a difference at least two. Furthermore, every two vertices u, v that have a distance two must have a label with a difference at least one. This study discusses the L(2,1) labeling on a lollipop graph L(m,n) with m ≥ 3 and n positive integers. The purpose of this study is to determine the minimum span value from the L(2,1) labeling on the lollipop graph Lm,n and we can symbolize λ2,1(Lm,n) and to determine the minimum span value from the L(2,1) labeling on the pendulum graph. In addition, it also builds a simulation program for L(2,1) labeling lollipop graphs up to tremendous values of m and n. In this paper, we obtained that the minimum span of a lollipop graph is λ2,1 (Lm,n) = 2m − 2, and the minimum span of a pendulum graph, let with k ≥ 4 and n ≥ 5, is k + 1.
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Cite this article
TY - CONF AU - Kusbudiono AU - Irham Af’idatul Umam AU - Ikhsanul Halikin AU - Mohamat Fatekurohman PY - 2022 DA - 2022/02/08 TI - L(2,1) Labeling of Lollipop and Pendulum Graphs BT - Proceedings of the International Conference on Mathematics, Geometry, Statistics, and Computation (IC-MaGeStiC 2021) PB - Atlantis Press SP - 44 EP - 47 SN - 2352-538X UR - https://doi.org/10.2991/acsr.k.220202.010 DO - 10.2991/acsr.k.220202.010 ID - 2022 ER -