More classes of super cycle-antimagic graphs

A simple graph G = (V,E) admits an H-covering if every edge in E belongs to a subgraph of G isomorphic to a given graph H . Then the graph G admitting an H-covering is (a, d)-H-antimagic if there exists a bijection f : V ∪ E → {1, 2, . . . , |V | + |E|} such that, for all subgraphs ∗ Corresponding author. P. JAYANTHI ET AL. /AUSTRALAS. J. COMBIN. 67 (1) (2017), 46–64 47 H ′ of G isomorphic to H , the H ′-weights, wtf(H ′) = ∑ v∈V (H′) f(v) + ∑ e∈E(H′) f(e), form an arithmetic progression a, a + d, a + 2d, . . . , a + (t − 1)d where a is the first term, d is the common difference and t is the number of subgraphs of G isomorphic to H . Such a labeling is called super if f(V ) = {1, 2, . . . , |V |}. This paper deals with some results on anti-balanced sets and we show the existence of super (a, d)-cycle-antimagic labelings of fans and some square graphs.