Article
On the Girth and Diameter of Generalized Johnson Graphs
Discrete Mathematics
Document Type
Post-Print
Publication Date
1-1-2018
Subjects
- Johnson graphs,
- Diameter (Geometry),
- Uniform subset graphs,
- Set theory
Disciplines
Abstract
Let v > k > i be non-negative integers. The generalized Johnson graph, J(v,k,i), is the graph whose vertices are the k-subsets of a v-set, where vertices A and B are adjacent whenever |A∩B|= i. In this article, we derive general formulas for the girth and diameter of J(v,k,i). Additionally, we provide a formula for the distance between any two vertices A and B in terms of the cardinality of their intersection.
DOI
10.1016/j.disc.2017.08.022
Persistent Identifier
http://archives.pdx.edu/ds/psu/23488
Citation Information
Louis Anthony Agong, Carmen Amarra, John Caughman, Ari J. Herman, et al.. "On the Girth and Diameter of Generalized Johnson Graphs" Discrete Mathematics Vol. 341 Iss. 1 (2018) p. 138 - 142 ISSN: 0012-365X Available at: http://works.bepress.com/john_caughman/28/
© 2017. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
NOTICE: this is the author’s version of a work that was accepted for publication in Discrete Mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Discrete Mathematics, 57, (January 2018). http://dx.doi.org/10.1016/j.disc.2017.08.022