Vol. 9, No. 4, 2016

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ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
Prime vertex labelings of several families of graphs

Nathan Diefenderfer, Dana C. Ernst, Michael G. Hastings, Levi N. Heath, Hannah Prawzinsky, Briahna Preston, Jeff Rushall, Emily White and Alyssa Whittemore

Vol. 9 (2016), No. 4, 667–688
Abstract

A simple and connected n-vertex graph has a prime vertex labeling if the vertices can be injectively labeled with the integers 1,2,3,,n such that adjacent vertices have relatively prime labels. We will present previously unknown prime vertex labelings for new families of graphs, including cycle pendant stars, cycle chains, prisms, and generalized books.

Keywords
graph labeling, prime vertex labeling, prime graphs
Mathematical Subject Classification 2010
Primary: 05C78
Milestones
Received: 21 March 2015
Revised: 12 August 2015
Accepted: 17 August 2015
Published: 6 July 2016

Communicated by Joseph A. Gallian
Authors
Nathan Diefenderfer
Northern Arizona University
Flagstaff, AZ 86011
United States
Dana C. Ernst
Northern Arizona University
Flagstaff, AZ 86001
United States
Michael G. Hastings
Northern Arizona University
Flagstaff, AZ 86011
United States
Levi N. Heath
Northern Arizona University
Flagstaff, AZ 86011
United States
Hannah Prawzinsky
Northern Arizona University
Flagstaff, AZ 86011
United States
Briahna Preston
Northern Arizona University
Flagstaff, AZ 86011
United States
Jeff Rushall
Northern Arizona University
Flagstaff, AZ 86011
United States
Emily White
Northern Arizona University
Flagstaff, AZ 86011
United States
Alyssa Whittemore
Northern Arizona University
Flagstaff, AZ 86011
United States