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 ) + ∑ u v ∈ E f ( u v ) = 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.