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Classification of 2-arc-transitive dihedrants
Shao Fei Du, Aleksander Malnič, Dragan Marušič, 2008, original scientific article

Abstract: 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 ▫${\mathbb{F}}_q$▫.
Found in: osebi
Keywords: permutation group, imprimitive group, dihedral group, Cayley graph, dihedrant, 2-Arc-transitive graph
Published: 15.10.2013; Views: 1801; Downloads: 57
URL Full text (0,00 KB)

Classification of regular embeddings of n-dimensional cubes
Shao Fei Du, Marston D. E. Conder, Stephen Wilson, Roman Nedela, Domenico A. Catalano, Young Soo Kwon, 2011, original scientific article

Found in: osebi
Keywords: cube, classification, regular embedding
Published: 15.10.2015; Views: 1410; Downloads: 79
URL Full text (0,00 KB)

Lovász Hamiltonicity Problem
Klavdija Kutnar, Shao Fei Du, Dragan Marušič, 2019, published scientific conference contribution abstract (invited lecture)

Found in: osebi
Keywords: Lovász problem, Hamilton cycle, vertex-transitive graph
Published: 06.08.2019; Views: 270; Downloads: 20
.pdf Full text (19,29 KB)
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Polynomials of degree 4 over finite fields representing quadratic residues
Shao Fei Du, Klavdija Kutnar, Dragan Marušič, 2019, original scientific article

Found in: osebi
Keywords: finite field, polynomial, quadratic residues
Published: 11.02.2020; Views: 78; Downloads: 14
URL Full text (0,00 KB)

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