Super(a,d)-star-antimagic graphs

Abstract

A simple graph G = (V, E) admitting an H-covering is said to be (a, d)-H-antimagic if there exists a bijection f : V ∪ E → {1, 2, . . . , |V | + |E|} such that, for all subgraphs H′ of G isomorphic to H, wtf (H′) = ∑v∈V (H′)f(v) + ∑e∈E(H′)f(e), form an arithmetic progression a, a+d, . . . , a+(t−1)d, where a is the first term, d is the common difference and t is the number of subgraphs in the H-covering. Then f is called an (a, d)-H-antimagic labeling. If f(V ) = {1, 2, . . . , |V |}, then f is called super (a, d)-H-antimagic labeling. In this paper we investigate the existence of super (a,d)-star-antimagic labelings of a particular class of banana trees and construct a star-antimagic graph.