L(2,1) Labeling of Lollipop and Pendulum Graphs

DOI

10.2991/acsr.k.220202.010How to use a DOI?

Keywords

L(2, 1) Labeling; Lollipop graph; Pendulum graph

Abstract

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 L_m,n and we can symbolize λ_2,1(L_m,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 λ_2,1 (L_m,n) = 2m − 2, and the minimum span of a pendulum graph, let P nk with k ≥ 4 and n ≥ 5, is k + 1.

Copyright

© 2022 The Authors. Published by Atlantis Press International B.V.

Open Access

This is an open access article under the CC BY-NC license.

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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  -