H-Coverings of Path-Amalgamated Ladders and Fans

Abstract EN

Let G be a connected, simple graph with finite vertices v and edges e.

A family G1,G2,…,Gp⊂G of subgraphs such that for all e∈E, e∈Gl, for some l, l=1,2,…,p is an edge-covering of G.

If Gl≅ℍ, ∀l, then G has an ℍ-covering.

Graph G with ℍ-covering is an ad,d-ℍ-antimagic if ψ:VG∪EG⟶1,2,…,v+e a bijection exists and the sum over all vertex-weights and edge-weights of ℍ forms a set ad,ad+d,…,ad+p−1d.

The labeling ψ is super for ψVG=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.