On super (a, d)-edge-antimagic total labeling of subdivided caterpillar

摘要

Let G = (V, E) be a graph with v vertices and e edges. An (a, d)-edge-antimagic total labeling is a bijection lambda from V (G) boolean OR E(G) to the set of consecutive integers 1, 2,..., v + e, such that the edge-weights {w(xy) : w(xy) = lambda(x) + lambda(y) + lambda(xy), xy is an element of E(G)} form an arithmetic progression with the initial term a and common difference d. Additionally, if lambda(V (G)) = {1, 2,..., v} then the labeling lambda is super (a, d)-edge-antimagic total. In this paper we investigate super (a, d)-edge-antimagic total labelings for subdivided caterpillars.