On the independence and domination numbers of replacement product graphs

Jay Cummings, Christine A. Kelley

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)181-194
Number of pages14
Issue number2
StatePublished - 2016


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

ASJC Scopus subject areas

  • General Mathematics


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