On Super Antimagicness of Generalized Flower and Disk Brake Graphs

摘要

Let G be a simple graph of order vertical bar V vertical bar and size vertical bar E vertical bar. An (a, d)-edge-antimagic total labeling of G is a one-to-one mapping f taking the vertices and edges onto {1, 2,..., vertical bar V vertical bar + vertical bar E vertical bar} such that the edge weights w(uv) = f(u) + f(v) + f(uv), uv is an element of E(G) form an arithmetic sequence {a, a + d,..., a + (vertical bar E vertical bar) - 1)d}, where the first term a > 0 and the common difference d >= 0. Such a labeling is called super if the smallest possible labels appear on the vertices.