Labelling of Generalized Friendship, Windmill, and Torch Graphs with a Condition at Distance Two
- 10.2991/acsr.k.220202.008How to use a DOI?
- L(2,1)-labelling; Labelling graph with distance two; Minimum of span; Generalized friendship; Windmill; Torch graph
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.
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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 -