A Study on Magic Labeling Regular Graph

Authors(2) :-P. Vivegananthan , B. Senthilkumar

Let G(V, E) be a graph and λ be a bisection from the set V ∪ E to the set of the first |V | + |E| natural numbers. The weight of a vertex is the sum of its label and the labels of all adjacent edges. We say λ is a vertex magic total (VMT) labeling of G if the weight of each vertex is constant. We say λ is an (s, d) -vertex anti-magic total (VAT) labeling if the vertex weights form an arithmetic progression starting at s with difference d . J. MacDougall conjectured that any regular graph with the exception of K2 and 2K3 has a VMT labeling. We give constructions of VAT labelings of any even-regular graphs and VMT labelings of certain regular graphs.

Authors and Affiliations

P. Vivegananthan
Department of Mathematics, PRIST University, Thanjavur, Tamil Nadu, India
B. Senthilkumar
Department of Mathematics, PRIST University, Thanjavur, Tamil Nadu, India

Graph Labeling, Vertex Magic Total Labeling, Vertex Antimagic Total Labeling.

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Publication Details

Published in : Volume 2 | Issue 4 | July-August 2017
Date of Publication : 2017-08-31
License:  This work is licensed under a Creative Commons Attribution 4.0 International License.
Page(s) : 615-620
Manuscript Number : CSEIT1724163
Publisher : Technoscience Academy

ISSN : 2456-3307

Cite This Article :

P. Vivegananthan , B. Senthilkumar , "A Study on Magic Labeling Regular Graph", International Journal of Scientific Research in Computer Science, Engineering and Information Technology (IJSRCSEIT), ISSN : 2456-3307, Volume 2, Issue 4, pp.615-620, July-August-2017.
Journal URL : http://ijsrcseit.com/CSEIT1724163

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