Vertex Magic Total labeling in Hamiltonian graphs

Abstract

A vertex magic total labeling on a graph with 12v ">  vertices and 12 e">  edges is a one - to - one map taking the vertices and edges onto the integers 121, 2, 3,…v +e">  with the property that the sum of the label on the vertex and the labels of its incident edges is constant, independent of the choice of the vertex. It is proved that all cycles have vertex magic total labeling. The Hamiltonian graphs have necessarily a cycle in it. Hence we study the relation of vertex magic total labeling in Hamiltonian graphs.