H-Coverings of Path-Amalgamated Ladders and Fans

Abstract

Let G be a connected, simple graph with finite vertices v and edges e . A family G 1 , G 2 , … , G p ⊂ G of subgraphs such that for all e ∈ E , e ∈ G l , for some l , l = 1,2 , … , p is an edge-covering of G . If G l ≅ ℍ , ∀ l , then G has an ℍ -covering. Graph G with ℍ -covering is an a d , d - ℍ -antimagic if ψ : V G ∪ E G ⟶ 1,2 , … , v + e a bijection exists and the sum over all vertex-weights and edge-weights of ℍ forms a set a d , a d + d , … , a d + p − 1 d . The labeling ψ is super for ψ V G = 1,2,3 , … , v and graph G is ℍ -supermagic for d = 0 . This manuscript proves results about super ℍ -antimagic labeling of path amalgamation of ladders and fans for several differences.