Title: L(2, 1) and surjective L(2, 1) labelling of Cartesian product between two complete bipartite graphs

Authors: Sumonta Ghosh; Anita Pal

Addresses: Department of Mathematics, NIT Durgapur, W. Bengal, 713209, India ' Department of Mathematics, NIT Durgapur, W. Bengal, 713209, India

Abstract: As we expect effective and efficient communication over a complex network, we consider the graph G = K_m,n × K_p,q to label with L(2, 1) labelling and investigate the bound λ_2,1 (G) in terms of m, n. We also raise few demerits of L(2, 1) labelling and introduced surjective L(2, 1) labelling as remedy. Surjective L(2, 1) labelling follows the restriction of L(2, 1) labelling where all the labels are unique and belongs to cardinality of the vertices in the graph. We also apply surjective L(2, 1) labelling on the graph G = K_m,n × K_p,q. In this paper we designed three different algorithms to incorporate above labelling and also analysed time complexity of the algorithms.

Keywords: Cartesian product; L(2, 1) labelling; surjective L(2, 1) labelling; complete bipartite graph; intelligence.

DOI: 10.1504/IJAIP.2025.147916

International Journal of Advanced Intelligence Paradigms, 2025 Vol.30 No.4, pp.334 - 349

Received: 21 Dec 2018
Accepted: 20 Feb 2019
Published online: 08 Aug 2025 *

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