Characterization of connected Vertex Magic Total labeling graphs in Topological ideals

A graph with v vertices and e edges is said to be vertex magic total labeling graph if there is a one to one map taking the vertices and edges onto the integers 1,2,+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. An ideal space is a triplet, where X is a nonempty set, Ï„ is a topology, I is an ideal of subsets of X. In this paper we characterize connected vertex magic total labeling graphs through the ideals in topological spaces. Keywords: Vertex magic total labeling graphs, ideal, topological space, Euler graph

Vertex Magic Total labeling in Hamiltonian graphs

A vertex magic total labeling on a graph with vertices and edges is a one - to - one map taking the vertices and edges onto the integers , , , … + 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