On the antimagic labeling of $(1,q)$-polar and $(1,q)$-decomposable graphs

In this paper the graphs yielded by the Algebraic Graph Decomposition theory are used to study the Hartsfield-Ringel conjecture on the antimagicness of connected graphs. This way some results on the conjecture are obtained, namely the antimagicness of connected $(1,2)$-polar and $(1,2)$-decomposable graphs, as well as connected $(1,q)$-polar and $(1,q)$-decomposable graphs satisfying some specific conditions.