Classification of 2-arc-transitive dihedrants

Du, Shao Fei; Malnič, Aleksander; Marušič, Dragan

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Naslov:	Classification of 2-arc-transitive dihedrants
Avtorji:	ID Du, Shao Fei (Avtor) ID Malnič, Aleksander (Avtor) ID Marušič, Dragan (Avtor)
Datoteke:	http://dx.doi.org/10.1016/j.jctb.2008.02.007
Jezik:	Angleški jezik
Vrsta gradiva:	Delo ni kategorizirano
Tipologija:	1.01 - Izvirni znanstveni članek
Organizacija:	IAM - Inštitut Andrej Marušič
Opis:	A complete classification of 2-arc-transitive dihedrants, that is, Cayley graphs of dihedral groups is given, thus completing the study of these graphs initiated by the third author in [D. Marušič, On 2-arc-transitivity of Cayley graphs, J. Combin. Theory Ser. B 87 (2003) 162-196]. The list consists of the following graphs: (i) cycles $C_{2n},\; n \ge 3$ ; (ii) complete graphs $K_{2n}, \; n \ge 3$ ; (iii) complete bipartite graphs $K_{n,n}, \; n \ge 3$ ; (iv) complete bipartite graphs minus a matching $K_{n,n} - nK_2, \; n \ge 3$ ; (v) incidence and nonincidence graphs $B(H_{11})$ and $B'(H_{11})$ of the Hadamard design on 11 points; (vi) incidence and nonincidence graphs $B(PG(d,q))$ and $B'(PG(d,q))$ , with $d \ge 2$ and $q$ a prime power, of projective spaces; (vii) and an infinite family of regular ${\mathbb{Z}}_d$ -covers $K_{q+1}^{2d}$ of $K_{q+1, q+1} - (q+1)K_2$ , where $q \ge 3$ is an odd prime power and $d$ is a divisor of $\frac{q-1}{2}$ and $q-1$ , respectively, depending on whether $q \equiv 1 \pmod{4}$ or $q \equiv 3 \pmod{4}$ obtained by identifying the vertex set of the base graph with two copies of the projective line $PG(1,q)$ , where the missing matching consists of all pairs of the form $[i,i']$ , $i \in PG(1,q)$ , and the edge $[i,j']$ carries trivial voltage if $i=\infty$ or $j=\infty$ , and carries voltage $\bar{h} \in {\mathbb{Z}}_d$ , the residue class of $h \in {\mathbb{Z}}_d$ , if and only if $i-j = \theta^h$ , where $\theta$ generates the multiplicative group ${\mathbb{F}}_q^\ast$ of the Galois field ${\mathbb{F}}_q$ .
Ključne besede:	permutation group, imprimitive group, dihedral group, Cayley graph, dihedrant, 2-Arc-transitive graph
Leto izida:	2008
Št. strani:	str. 1349-1372
Številčenje:	Vol. 98, iss. 6
PID:	20.500.12556/RUP-965
ISSN:	0095-8956
UDK:	519.17
COBISS.SI-ID:	2018277
Datum objave v RUP:	15.10.2013
Število ogledov:	4286
Število prenosov:	93
Metapodatki:
:	DU, Shao Fei, MALNIČ, Aleksander in MARUŠIČ, Dragan, 2008, Classification of 2-arc-transitive dihedrants. [na spletu]. 2008. Vol. 98, no. 6, p. 1349–1372. [Dostopano 8 april 2025]. Pridobljeno s: http://dx.doi.org/10.1016/j.jctb.2008.02.007 Kopiraj citat