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, wt f (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 starantimagic graph.

H-Coverings of Path-Amalgamated Ladders and Fans

“…Susanto [7] derived bound for cycle-antimagic labeling of disjoint union of cycles. Recent results on H-antimagic labeling of graphs can be seen in [8][9][10][11][12][13][14]. Also, in [12], Baca et al discussed the tree-antimagicness of disconnected graphs.…”