2-PRODUCT CORDIAL LABELLING OF K-REGULAR BIPARTITE GRAPHS

This article explores the concept of p-product cordial labeling of graphs, which generalizes the well-established notion of cordial labeling. Cordial labeling techniques have significant applications in various fields such as cryptography, neural networks, artificial intelligence, chemistry, and network modelling. In this study, we define p-product cordial labeling as a vertex labeling function ?: V (G) ? {0, 1, …, p ? 1}, where p ? N and p ? |V (G)|, with an induced edge labeling ??: E(G) ? {0, 1, …, p ? 1} given by ?? (uv) = ?(u) · ?(v) mod p. A labeling ? is said to be p-product cordial if, for all labels i and j, the number of vertices labeled i and j differ by at most one, and similarly, the number of edges labeled i and j differ by at most one. The paper specifically investigates the 2-product cordiality of k-regular bipartite graphs. It is shown that every 1-regular bipartite graph is 2-product cordial. Further, the study presents conditions under which general k-regular bipartite graphs are 2-product cordial and identifies cases where such cordiality does not hold. © 2025 KSCAM.