On the Girth and Diameter of Generalized Johnson Graphs

Authors

Louis Anthony Agong, University of the Philippines
Carmen Amarra, University of the Philippines
John Caughman, Portland State UniversityFollow
Ari J. Herman, Portland State University
Taiyo S. Terada, Portland State University

Published In

Discrete Mathematics

Document Type

Post-Print

Publication Date

1-1-2018

Subjects

Johnson graphs, Diameter (Geometry), Uniform subset graphs, Set theory

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.

Description

© 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

DOI

10.1016/j.disc.2017.08.022

Persistent Identifier

http://archives.pdx.edu/ds/psu/23488

Citation Details

Agong, Louis Anthony; Amarra, Carmen; Caughman, John; Herman, Ari J.; and Terada, Taiyo S., "On the Girth and Diameter of Generalized Johnson Graphs" (2018). Mathematics and Statistics Faculty Publications and Presentations. 201.
http://archives.pdx.edu/ds/psu/23488