<i>L</i>(2, 1) and surjective <i>L</i>(2, 1) labelling of Cartesian product between two complete bipartite graphs

As we expect effective and efficient communication over a complex network, we consider the graph G = Km,n × Kp,q to label with L(2, 1) labelling and investigate the bound λ2,1 (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 = Km,n × Kp,q. In this paper we designed three different algorithms to incorporate above labelling and also analysed time complexity of the algorithms.