Ladders and fan graphs are cycle-antimagic

Abstract

A simple graph G = (V, E) admits an H-covering if every edge in E belongs to at least one subgraph of G isomorphic to a given graph H. 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 H ′ of G isomorphic to H, the H ′-weights, wt f (H ′) = ∑ v∈V (H ′) f (v) + ∑ e∈E(H ′) f (e), form an arithmetic progression with the initial term a and the common difference d. Such a labeling is called super if the smallest possible labels appear on the vertices. In this paper we prove the existence of super (a, d)-H-antimagic labelings of fan graphs and ladders for H isomorphic to a cycle.

On H-antimagic coverings for m-shadow and closed m-shadow of connected graphs

“…nected graphs. Some graphs belonging to cycle-antimagic graph were given in [4,5,6,7,8]. For more results related to 𝐻 -antimagicness of graphs, one can see [9,10].…”

“…Bača et al in [3] investigated the H -antimagicness of disconnected graphs. Some graphs belonging to cycle-antimagic graph were given in [4] , [5] , [6] , [7] , [8] . For more results related to H -antimagicness of graphs, one can see [9] , [10] .…”