Open AccessIntegral Cayley graphs over semi-dihedral groups
Author(s) -
T.C.E. Cheng,
Lihua Feng,
Guihai Yu,
Chi Zhang
Publication year - 2023
Publication title -
applicable analysis and discrete mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.69
H-Index - 26
eISSN - 2406-100X
pISSN - 1452-8630
DOI - 10.2298/aadm190330001c
Subject(s) - cayley graph , dihedral group , mathematics , combinatorics , dihedral angle , chordal graph , discrete mathematics , cayley transform , character (mathematics) , group (periodic table) , graph , line graph , voltage graph , hydrogen bond , chemistry , geometry , organic chemistry , molecule
Classifying integral graphs is a hard problem that initiated by Harary and Schwenk in 1974. In this paper, with the help of character table, we treat the corresponding problem for Cayley graphs over the semi-dihedral group SD8n = ?a,b | a4n = b2 = 1; bab = a2n-1?, n ? 2. We present several necessary and sufficient conditions for the integrality of Cayley graphs over SD8n, we also obtain some simple sufficient conditions for the integrality of Cayley graphs over SD8n in terms of the Boolean algebra of hai. In particular, we give the sufficient conditions for the integrality of Cayley graphs over semi-dihedral groups SD2n (n?4) and SD8p for a prime p, from which we determine several infinite classes of integral Cayley graphs over SD2n and SD8p.