SET-CORDIALITY INDEX OF BIPARTITE GRAPHS VIA BOOLEAN LAYERS AND HYPERCUBE EMBEDDINGS
We study the set-cordiality index of graphs, a set-valued labeling parameter introduced by Naduvath [7], and develop a general framework for bipartite graphs. A universal lower bound is established in terms of the larger partite class, along with a sufficient condition for its attainment using three consecutive layers of the Boolean lattice. To handle cases beyond this criterion, we introduce a hypercube subgraph principle, which links set-cordial labelings to graph embeddings in hypercubes. As applications, we determine exact set-cordiality indices for ladder graphs and even prism graphs, and a couple of additional results by direct arguments rather than the established principle. The results highlight the role of Boolean layer capacities and embedding structures, and we conclude with conjectures for trees and Cartesian product graphs.