Super (a, d)-Edge-Antimagic Total Labeling of Subdivided Stars and w-trees

摘要

Kotzig and Rosa (1970) conjectured that every tree is an edge-magic graph. Furthermore, Enomoto, Llado, Nakamigawa and Ringel (1998), proposed the conjecture that every tree admits a super (a, 0)-edge-antimagic total labeling. In this paper, we give support to the partial correctness of these conjectures by showing that subdivided stars and subdivided w-trees are super (a, 0)-edgeantimagic total graphs. Also, we prove that these graphs are super (a, d)-edge-antimagic total for some d not equal 0.