On Perfect 2‐Colorings of Johnson Graphs J(v, 3). Issue 6 (30th July 2012)

• Record Type: Journal Article
• Authors: Gavrilyuk, Alexander L.; Goryainov, Sergey V.
• Is Part Of: Journal of combinatorial designs. Volume 21:Issue 6(2013:Jun.)
• Page Start: 232
• Page End: 252
• Publication Date: 2012-07-30
• Subjects: Combinatorial designs and configurations -- Periodicals; Configurations et schémas combinatoires -- Périodiques; 511.6
• DOI: 10.1002/jcd.21327
• Languages: English
• ISSNs: 1063-8539

Abstract

<abstract abstract-type="main"> <title>Abstract</title> <p>We study the perfect 2‐colorings (also known as the equitable partitions into two parts or the completely regular codes with covering radius 1) of the Johnson graphs <inline-graphic mimetype="image" xlink:href="ark:/27927/pgg1x5tz9wx" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:10638539:media:jcd21327:jcd21327-math-0003" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>J</mml:mi><mml:mo>(</mml:mo><mml:mi>v</mml:mi><mml:mo>, </mml:mo><mml:mn>3</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math>. In particular, we classify all the realizable quotient matrices of perfect 2‐colorings for odd <italic>v</italic>. © 2012 Wiley Periodicals, Inc. J. Combin. Designs 21: 232–252, 2013</p> </abstract>