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

Ikhsanul Halikin, Hafif Komarullah · Advances in computer science research · 2022

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. Keywords: 𝐿(2,1

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