Vertex Magic Total labeling in Hamiltonian graphs

R. Senthil Amutha; N. Murugesan

R. Senthil Amutha Head and Assistant Professor, Department of Mathematics, Sree Saraswathi thyagaraja College, Pollachi-642107, India
N. Murugesan Assistant Professor at Department of Mathematics, Sree Saraswathi Thyagaraja College, Pollachi, India

Keywords: edge magic total labeling, vertex magic total labeling, Hamiltonian graphs, magic constant.

Abstract

A vertex magic total labeling on a graph with 𝒗 vertices and 𝒆 edges is a one - to - one map taking the vertices and edges onto the integers 𝟏, 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.

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