Vol. 3, No. 2, 2010

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Minimal $k$-rankings for prism graphs

Juan Ortiz, Andrew Zemke, Hala King, Darren Narayan and Mirko Horňák

Vol. 3 (2010), No. 2, 183–190
Abstract

We determine rank numbers for the prism graph P2 × Cn (P2 being the connected two-node graph and Cn a cycle of length n) and for the square of an even cycle.

Keywords
$k$-rankings, vertex coloring, prism graphs
Mathematical Subject Classification 2000
Primary: 05C15, 05C78
Secondary: 05C69, 05C35
Milestones
Received: 25 March 2009
Revised: 15 April 2010
Accepted: 15 April 2010
Published: 11 August 2010

Communicated by Vadim Ponomarenko
Authors
Juan Ortiz
Department of Mathematics
Lehigh University
Bethlehem, PA 18015
United States
Andrew Zemke
School of Mathematical Sciences
Rochester Institute of Technology
85 Lomb Memorial Drive
Rochester, NY 14623
United States
Hala King
Mathematics Department
California Lutheran University
Thousand Oaks, CA 91360
United States
Darren Narayan
School of Mathematical Sciences
Rochester Institute of Technology
85 Lomb Memorial Drive
Rochester, NY 14623
United States
http://people.rit.edu/~dansma/
Mirko Horňák
Institute of Mathematics
P.J. Šafá rik University
Jesenná 5, 040 01
Košice, Slovakia