Vol. 10 No. 1 (2011): Mapana Journal of Sciences
Research Articles

Split and Non-Split Dominator Chromatic Numbers and Related Parameters

  • K Kavitha,
  • N G David,
  • N. Selvi
K Kavitha
Department of Mathematics, Madras Christian College, Chennai 600 059
N G David
Department of Mathematics, Madras Christian College, Chennai 600 059
N. Selvi
Department of Mathematics, A.D.M. College for Women Nagapattinam, Tamil Nadu – 611 001;
DOI: https://doi.org/10.12723/mjs.18.5

Published 2021-08-26

Copyright (c) 2011

Creative Commons License

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

Abstract

A proper graph coloring is defined as coloring the nodes of a graph with the minimum number of colors without any two adjacent nodes having the same color.  Dominator coloring of G is a proper coloring in which every vertex of G dominates every vertex of at least one color class.  In this paper, new parameters, namely strong split and non-split dominator chromatic numbers and block, cycle, path non-split dominator chromatic numbers are introduced.  These parameters are obtained for different classes of graphs and also interesting results are established.

References

  1. S. Arumugam, On dominator coloring in graphs, IWGC, BDU, 2010.
  2. V.R. Kulli, Theory of Domination in Graphs, Vishwa International Publication, Gulbarga, India, 2010.
  3. V.R. Kulli and B. Janakiram, The strong split domination number of a graph, Acta Ciencia Indica, 32M (2006) 715-720.
  4. V.R. Kulli and B. Janakiram, The strong non-split domination number of a graph, Internat. J. Management Systems, 19 (2003) 145-156.
  5. V.R. Kulli and B. Janakiram, The block non-split domination number of a graph, Internat.J. Management Systems, 20 (2004) 219-228.