On Equality and Strong Equality of Domination Number and Independent Domination Number in Graphs

Authors

  • Pious Femlin Department of Mathematics, Christ University, Bangalore-560029, India
  • Joseph Mayamma Department of Mathematics, Christ University, Bangalore-560029, India;

DOI:

https://doi.org/10.12723/mjs.34.4

Keywords:

Domination, Independent domination, Efficient dominating set, Strong equality of domination parameters

Abstract

 

In this paper we explore graphs having same domination number and independent domination number . Such graphs are denoted as ( , )-graphs. Several families of  ( , )-graphs have been constructed. The realization problem for graphs with  =  = a for any given positive integer a has been solved. Furthermore, properties of graphs in which every  -set is a -set has been investigated.

Author Biographies

Pious Femlin, Department of Mathematics, Christ University, Bangalore-560029, India

Department of Mathematics, Christ University, Bangalore-560029, India

Joseph Mayamma, Department of Mathematics, Christ University, Bangalore-560029, India;

Department of Mathematics, Christ University, Bangalore-560029, India;

References

D. W. Bange , A. E. Barkauskas, L. H. Host and P.J. Slater, "Generalized domination and efficient domination in graphs," Discrete Math., vol. 159, no. 1, pp. 1-11, 1996.

T. W. Haynes , M. A. Henning and P. J. Slater, "Strong equality of domination parameters in trees," Discrete Math., vol. 206, no. 1-3, pp. 77-87, 2003.

T. W. Haynes and M. A. Henning, "Trees with large paired-domination number," Util. Math., vol. 71, no. 1, pp. 3-12, 2006.

T. W. Haynes and P. J. Slater, "Paired-domination in graphs, DiscreteMath., vol. 32, no. 3, pp. 199-206, 1998.

W. Goddard and M. A. Henning, J. Lyle and J. Southey, "On the independent domination in graphs", Ann. Comb., vol. 16, no. 4, pp. 719-732, 2012.

W. Goddard and M. A. Henning, "Independent domination in graphs: a survey and recent results", Discrete Math., vol. 313, no. 7, pp. 839-854, 2013.

Published

2021-08-28