L(2,1) Labeling of Lollipop and Pendulum Graphs
Date
2022-02-08Author
KUSBUDIONO, Kusbudiono
UMAM, Irham Af'idatul
HALIKIN, Ikhsanul
FATEKUROHMAN, Mohamat
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One of the topics in graph labeling is πΏ(2,1) labeling which is an extension of graph labeling. Definition of πΏ(2,1)
labeling is a function that maps the set of vertices in the graph to non-negative integers such that every two vertices π’, π£
that have a distance one must have a label with a difference at least two. Furthermore, every two vertices π’, π£ that have
a distance two must have a label with a difference at least one. This study discusses the πΏ(2,1) labeling on a lollipop
graph πΏπ,π with π β₯ 3 and π positive integers. The purpose of this study is to determine the minimum span value from
the πΏ(2,1) labeling on the lollipop graph πΏπ,π and we can symbolize π2,1(πΏπ,π) and to determine the minimum span
value from the πΏ(2,1) labeling on the pendulum graph. In addition, it also builds a simulation program for πΏ(2,1) labeling
lollipop graphs up to tremendous values of π and π. In this paper, we obtained that the minimum span of a lollipop
graph is π2,1(πΏπ,π) = 2π β2, and the minimum span of a pendulum graph, let ππ
π with π β₯ 4 and π β₯ 5, is π + 1.
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- LSP-Conference Proceeding [1877]