Title: L(2,2,1)-labelling problems on square of path

Authors: Sk Amanathulla; Madhumangal Pal

Addresses: Department of Mathematics, Raghunathpur College, Raghunathpur, 723133, India ' Department of Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, 721102, India

Abstract: L(p, q)-labelling problem is a well studied problem in the last three decades for its wide applications, specially in frequency assignment in (mobile) communication system, X-ray crystallography, coding theory, radar, astronomy, circuit design etc. L(2, 2, 1)-labelling is an extension of L(p, q)-labelling is now becomes a well studied problem due to its applications. Motivated from this point of view, we consider L(2, 2, 1)-labelling problem for squares of path. Let G = (V,E) be a graph. The L(2, 2, 1)-labelling of the graph G is a mapping η : V → {0, 1, 2, …} so that |η(x) - η(y)| ≥ 2 if d(x, y) = 1 or 2, |η(x) - η(y)| ≥ 1 if d(x, y) = 3, where V is the vertex set and d(x, y) is the distance (i.e. minimum number of edges in the shortest path between x and y) between the vertices x and y. λ_2,2,1(G) is the L(2, 2, 1)-labelling number of G, which is the largest non-negative integer which is used to label the graph G. In labelling problems of graph the main target is to find the exact value of λ_2,2,1(G) or to minimise it. In this paper, we have studied L(2, 2, 1)-labelling of squares of path and obtain a good result for it. Also a labelling procedure is presented to label a square of path. The result of this paper is exact and also it is unique. This is the first result about L(2, 2, 1)-labelling of squares of path.

Keywords: frequency assignment; L (2, 2, 1)-labelling; squares of path.

DOI: 10.1504/IJAIP.2024.142668

International Journal of Advanced Intelligence Paradigms, 2024 Vol.29 No.2/3, pp.211 - 224

Received: 29 Jun 2018
Accepted: 04 Aug 2019
Published online: 15 Nov 2024 *

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