On free α-labelings of cubic bipartite graphs

Abstract

It is known that an a-labeling of a bipartite graph G with n edges can be used to obtain a cyclic G-decomposition of K 2nx+1 for every positive integer x. It is also known that if two graphs G and H admit a free a-labeling, then their vertex-disjoint union also admits a free a-labeling. We show that if G is a bipartite prism, a bipartite Möbius ladder or a connected cubic bipartite graph of order at most 14, then G admits a free a-labeling. We conjecture that every bipartite cubic graph admits a free a-labeling.