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

# Labelling of Generalized Friendship, Windmill, and Torch Graphs with a Condition at Distance Two

Authors
Ikhsanul Halikin*, Hafif Komarullah
Graph, Combinatorics, and Algebra Research Group, Department of Mathematics, FMIPA, University of Jember
*Corresponding author. Email: ikhsan.fmipa@unej.ac.id
Corresponding Author
Ikhsanul Halikin
Available Online 8 February 2022.
DOI
10.2991/acsr.k.220202.008How to use a DOI?
Keywords
L(2,1)-labelling; Labelling graph with distance two; Minimum of span; Generalized friendship; Windmill; Torch graph
Abstract

A graph labelling with a condition at distance two was first introduced by Griggs and Robert. This labelling is also known as L(2,1)-labelling. Let G = (V, E) be a non-multiple graph, undirected, and connected. An L(2,1)-labelling on a graph is defined as a mapping from the vertex set V(G) to the set of nonnegative integer such that for x, yV(G), |f(x) − f(y)| ≥ 2 if d(x, y) = 1 and |f(x) − f(y)| ≥ 1 if d(x, y) = 2, where d(x, y) denoted the distance between vertex x and y. The largest number of the vertex labels is called as span of L(2.1)-labelling. The span of a graph G can be more than one, the minimum value of the span of a graph G is notated by λ(2,1) (G). In this paper, we consider a graph labelling with distance two on generalized friendship, windmill, and torch graphs.

© 2022 The Authors. Published by Atlantis Press International B.V.
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
Advances in Computer Science Research
Publication Date
8 February 2022
ISBN
10.2991/acsr.k.220202.008
ISSN
2352-538X
DOI
10.2991/acsr.k.220202.008How to use a DOI?
© 2022 The Authors. Published by Atlantis Press International B.V.
Open Access
This is an open access article under the CC BY-NC license.

TY  - CONF
AU  - Ikhsanul Halikin
AU  - Hafif Komarullah
PY  - 2022
DA  - 2022/02/08
TI  - Labelling of Generalized Friendship, Windmill, and Torch Graphs with a Condition at Distance Two
BT  - Proceedings of the  International Conference on Mathematics, Geometry, Statistics, and Computation (IC-MaGeStiC 2021)
PB  - Atlantis Press
SP  - 35
EP  - 39
SN  - 2352-538X
UR  - https://doi.org/10.2991/acsr.k.220202.008
DO  - 10.2991/acsr.k.220202.008
ID  - Halikin2022
ER  -