TY - JOUR

T1 - Perfect codes from PGL(2,5) in Star graphs

AU - Mogilnykh, Ivan Yurevich

N1 - Funding Information: Mogilnykh, I. Yu., Perfect codes from PGL(2,5) in Star graphs. ⃝c 2020 Mogilnykh I.Yu. This work was partially supported by the Grant RFBR 18-01-00353A. Publisher Copyright: © 2020 mogilnykh i.yu. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020

Y1 - 2020

N2 - The Star graph Snis the Cayley graph of the symmetric group Sym„ with the generating set {(1 i) : 2 < i < n}. Arumugam and Kala proved that {π Є Sym„: π(1) = 1} is a perfect code in Snfor any n, n > 3. In this note we show that for any n, n > 6 the Star graph Sncontains a perfect code which is the union of cosets of the embedding of PGL(2,5) into Sym6.

AB - The Star graph Snis the Cayley graph of the symmetric group Sym„ with the generating set {(1 i) : 2 < i < n}. Arumugam and Kala proved that {π Є Sym„: π(1) = 1} is a perfect code in Snfor any n, n > 3. In this note we show that for any n, n > 6 the Star graph Sncontains a perfect code which is the union of cosets of the embedding of PGL(2,5) into Sym6.

KW - Cayley graph

KW - efficient dominating set

KW - perfect code

KW - projective linear group

KW - Star graph

KW - symmetric group

KW - CAYLEY-GRAPHS

UR - http://www.scopus.com/inward/record.url?scp=85097216888&partnerID=8YFLogxK

U2 - 10.33048/semi.2020.17.034

DO - 10.33048/semi.2020.17.034

M3 - Article

AN - SCOPUS:85097216888

VL - 17

SP - 534

EP - 539

JO - Сибирские электронные математические известия

JF - Сибирские электронные математические известия

SN - 1813-3304

ER -