Antimagic labellings of (k, 2)-bipartite biregular graphs

Abstract

An antimagic labelling of a graph is a bijection from the set of edges to $\{1,2,\dots ,m\}$, such that all vertex-sums are pairwise distinct, where the vertex-sum of a vertex is the sum of labels on the edges incident to it. We say a graph is antimagic if it has an antimagic labelling. In 2023, it has been proven that connected $(k,l)$-bipartite graphs are antimagic if $k\ge l+2$ and one of k or l is odd. In this paper, we extend this result to connected $(k,2)$-bipartite biregular graphs for $k\ge 4$ even, and to $(k,2)$-bipartite biregular graphs for $k\ge 3$ odd.

Generalization of the previous results for (3,2)-bipartite connected graphs