Vol. 9, No. 2, 2016

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ISSN: 1944-4184 (e-only)
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On the independence and domination numbers of replacement product graphs

Jay Cummings and Christine A. Kelley

Vol. 9 (2016), No. 2, 181–194
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.

Keywords
minimized domination number, total domination number, maximized independence number, replacement product of a graph
Mathematical Subject Classification 2010
Primary: 05C10
Milestones
Received: 22 October 2011
Revised: 25 February 2015
Accepted: 26 February 2015
Published: 2 March 2016

Communicated by Joseph A. Gallian
Authors
Jay Cummings
Department of Mathematics
University of California, San Diego
La Jolla, CA 92093
United States
Christine A. Kelley
Department of Mathematics
University of Nebraska–Lincoln
Lincoln, NE 68588
United States