Open Access
2018 Labeling crossed prisms with a condition at distance two
Matthew Beaudouin-Lafon, Serena Chen, Nathaniel Karst, Jessica Oehrlein, Denise Troxell
Involve 11(1): 67-80 (2018). DOI: 10.2140/involve.2018.11.67

Abstract

An L(2,1)-labeling of a graph is an assignment of nonnegative integers to its vertices such that adjacent vertices are assigned labels at least two apart, and vertices at distance two are assigned labels at least one apart. The λ-number of a graph is the minimum span of labels over all its L(2,1)-labelings. A generalized Petersen graph (GPG) of order n consists of two disjoint cycles on n vertices, called the inner and outer cycles, respectively, together with a perfect matching in which each matching edge connects a vertex in the inner cycle to a vertex in the outer cycle. A prism of order n3 is a GPG that is isomorphic to the Cartesian product of a path on two vertices and a cycle on n vertices. A crossed prism is a GPG obtained from a prism by crossing two of its matching edges; that is, swapping the two inner cycle vertices on these edges. We show that the λ-number of a crossed prism is 5, 6, or 7 and provide complete characterizations of crossed prisms attaining each one of these λ-numbers.

Citation

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Matthew Beaudouin-Lafon. Serena Chen. Nathaniel Karst. Jessica Oehrlein. Denise Troxell. "Labeling crossed prisms with a condition at distance two." Involve 11 (1) 67 - 80, 2018. https://doi.org/10.2140/involve.2018.11.67

Information

Received: 9 July 2016; Revised: 18 August 2016; Accepted: 7 September 2016; Published: 2018
First available in Project Euclid: 20 December 2017

zbMATH: 1369.05064
MathSciNet: MR3681348
Digital Object Identifier: 10.2140/involve.2018.11.67

Subjects:
Primary: 68R10 , 94C15
Secondary: 05C15 , 05C78

Keywords: channel assignment , distance two labeling , generalized Petersen graph , L(2,1)-coloring , L(2,1)-labeling

Rights: Copyright © 2018 Mathematical Sciences Publishers

Vol.11 • No. 1 • 2018
MSP
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