Proceedings of the International Conference on Mathematics, Geometry, Statistics, and Computation (IC-MaGeStiC 2021)

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

Authors
Kusbudiono*, Irham Af’idatul Umam, Ikhsanul Halikin, Mohamat Fatekurohman
Graph, Combinatorics, and Algebra Research Group, Department of Mathematics, FMIPA, Universitas Jember
*Corresponding author. Email: kusbudiono@unej.ac.id
Corresponding Author
Kusbudiono
Available Online 8 February 2022.
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 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 P nk with k ≥ 4 and n ≥ 5, is k + 1.

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

Volume Title
Proceedings of the International Conference on Mathematics, Geometry, Statistics, and Computation (IC-MaGeStiC 2021)
Series
Publication Date
8 February 2022
ISBN
10.2991/acsr.k.220202.010
ISSN
2352-538X
DOI
10.2991/acsr.k.220202.010How to use a DOI?
Open Access
This is an open access article under the CC BY-NC license.

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  -