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

^{*}, Hafif Komarullah

^{*}Corresponding author. Email: ikhsan.fmipa@unej.ac.id

- 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, y*∈*V*(*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.- 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.

### Cite this article

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 -