Involve: A Journal of Mathematics

  • Involve
  • Volume 9, Number 2 (2016), 181-194.

On the independence and domination numbers of replacement product graphs

Jay Cummings and Christine A. Kelley

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Abstract

This paper examines invariants of the replacement product of two graphs in terms of the properties of the component graphs. In particular, we present results on the independence number, the domination number, and the total domination number of these graphs. The replacement product is a noncommutative graph operation that has been widely applied in many areas. One of its advantages over other graph products is its ability to produce sparse graphs. The results in this paper give insight into how to construct large, sparse graphs with optimal independence or domination numbers.

Article information

Source
Involve, Volume 9, Number 2 (2016), 181-194.

Dates
Received: 22 October 2011
Revised: 25 February 2015
Accepted: 26 February 2015
First available in Project Euclid: 22 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.involve/1511370993

Digital Object Identifier
doi:10.2140/involve.2016.9.181

Mathematical Reviews number (MathSciNet)
MR3470724

Zentralblatt MATH identifier
1333.05087

Subjects
Primary: 05C10: Planar graphs; geometric and topological aspects of graph theory [See also 57M15, 57M25]

Keywords
minimized domination number total domination number maximized independence number replacement product of a graph

Citation

Cummings, Jay; Kelley, Christine A. On the independence and domination numbers of replacement product graphs. Involve 9 (2016), no. 2, 181--194. doi:10.2140/involve.2016.9.181. https://projecteuclid.org/euclid.involve/1511370993


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