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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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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.

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