E-Super Vertex Magic Regular Graphs of Odd Degree

Abstract

Let G=(V,E) be a finite simple graph with p vertices and q edges, without isolated vertices or isolated edges. A vertex magic total labeling is a bijection f from V∪E to the consecutive integers 1,2,⋯,p+q, with the property that, for every vertex u∈V, one has f(u)+∑uv∈Ef(uv)=k for some constant k. The vertex magic total labeling is called E-super if f(E)={1,2,⋯,q}. In this paper we verify the existence of E-super vertex magic total labeling for odd regular graphs containing a particular 3-factor.