A Study on Perfect 3 Coloring of Cubic Graph of Order 10

Authors

  • K S Dilip  M. Phil Scholar, Department of Mathematics, Dr. SNS. Rajalaksmi College of arts and science, Coimbatore, Tamilnadu, India
  • T. Ramesh  Assistant Professor, Department of Mathematics, Dr. SNS. Rajalaksmi College of arts and science, Coimbatore, Tamilnadu, India

Keywords:

Perfect Colouring, Parameter Matrix, Peterson Graphs.

Abstract

Perfect coloring is a generalization of the notion of completely regular code. This thesis entitled “ A STUDY OF PERFECT 3 COLORING OF CUBIC GRAPH OF  ORDER 10” examines the idea identified with perfectly coloring a cubic graph of order 10. A perfect m coloring of a graph G with m colors is a partition of vertex set of G into m parts A1, A 2, A 3 …..Am such that, for all i,j  every vertex of Ai is adjacent to the same number of vertices, namely, aij vertices of Aj and we classify the realizable coloring of parameter matrix (symmetric)of perfect 3-colorings for the cubic graph of order 10.

References

  1. M Alaeiyan and A. Abedi, Perfect 2-colorings of Johnson graphs J(4, 3), J(4, 3), J(6, 3) and Petersen graph, Ars Combinatoria, (to appear).
  2. FC. Bussemaker, S. Cobeljic, D.M. Cvetkovic and J.J. Seidel, Computer invetigation of cubic graphs, Technische Hpgesschool Eindhoven Nederland Onderafedeling Der Wiskunde, January 1976. 205 www.ejgta.org Perfect 3-colorings of the cubic graphs of order 10 | M. Alaeiyan and A. Mehrabani.
  3. SV. Avgustinovich and I. Yu. Mogilnykh, Perfect 2-colorings of Johnson graphs J(6, 3) and J(7, 3), Lecture Notes in Computer Science 5228 (2008), 11–19.
  4. DG. Fon-Der-Flaass, Perfect 2-colorings of a hypercube, Siberian Mathematical Journal 4 (2007), 923–930.

International Journal of Scientific Research in Science, Engineering and Technology

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Published

2018-07-30

Issue

Volume 4, Issue 9, July-August-2018

Section

Research Articles

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This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

[1]
K S Dilip, T. Ramesh, " A Study on Perfect 3 Coloring of Cubic Graph of Order 10, International Journal of Scientific Research in Science, Engineering and Technology(IJSRSET), Print ISSN : 2395-1990, Online ISSN : 2394-4099, Volume 4, Issue 9, pp.276-281, July-August-2018.