Super (a, d)-H-antimagic labeling of subdivided graphs

Abstract

A simple graph G = (V, E) admits an H-covering, if every edge in E(G) belongs to a subgraph of G isomorphic to H. A graph G admitting an H-covering is called an (a, d)-H-antimagic if there exists a bijective function f : V(G) ∪ E(G) → {1, 2, ⋯, /V(G)/ + /E(G)/} such that for all subgraphs H′ isomorphic to H the sums Σv∈V(H′)f(v) + Σe∈E(H′)f(e) form an arithmetic sequence {a, a + d, ⋯, a + (t - 1)d}, where a > 0 and d ≥ 0 are integers and t is the number of all subgraphs of G isomorphic to H. Moreover, if the vertices are labeled with numbers 1, 2, ⋯, /V(G)/ the graph is called super. In this paper we deal with super cycle-antimagicness of subdivided graphs. We also prove that the subdivided wheel admits an (a, d)-cycle-antimagic labeling for some d.