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.

  1. S. Arumugam and S. Velammal, Edge domination in graphs, Taiwanese Journal of Mathematics, Volume 2, Number 2, June 1998, 173 - 179.
  2. A. Nagoorgani and M. Basheer Ahamed, Order and Size in Fuzzy Graph, Bulletin of Pure and Applied Sciences, Volume 22E, Number 1, 2003, 145 - 148.
  3. Nagoor Gani and V. T. Chandrasekaran, A First Look at Fuzzy Graph Theory, Allied Publishers, 2010.
  4. Nagoor Gani and J. Malarvizhi, Properties of μ-Complement of a Fuzzy Graph, International Journal of Algorithms, Computing and Mathematics, Volume 2, Number 3, 2009, 73 - 83.
  5. NagoorGani and K. Radha, On regular fuzzy graphs, Journal of Physical Sciences, Volume 12, 2008, 33 - 44.
  6. Nagoorgani and K. Radha, The degree of a vertex in some fuzzy graphs, International Journal of Algorithms, Computing and Mathematics, Volume 2, Number 3, August 2009, 107 - 116.
  7. NagoorGani and K. Radha, Regular Property of Fuzzy Graphs, Bulletin of Pure and Applied Sciences, Volume 27E, Number 2, 2008, 411 - 419.
  8. K. Radha and N. Kumaravel, The degree of an edge in Cartesian product and composition of two fuzzy graphs, International Journal of Applied Mathematics & Statistical Sciences(IJAMSS) ©IASET, Vol. 2, Issue 2, May 2013, 65 - 78.
  9. K. Radha and N. Kumaravel, Some properties of edge regular fuzzy graphs, Jamal Academic Research Journal (JARJ), Special issue, 2014, 121 - 127

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. |          | BibTeX | RIS | CSV

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