arXiv subjects

István Kovács

Publications and source records attributed to István Kovács.

40 records · Page 3Linked to original sources

arXiv2013

The number of cyclic configurations of type $(v_3)$ and the isomorphism problem

A configuration of points and lines is cyclic if it has an automorphism which permutes its points in a full cycle. A closed formula is derived for the number of non-isomorphic connected cyclic configurations of type (v_3), i.e., which have v points and lines, and each point/line is incident with exactly 3 lines/points. In addition, a Bays-Lambossy type theorem is proved for cyclic configurations if the number of points is a product of two primes or a prime power.

math.CO↗

arXiv2012

Isomorphic tetravalent cyclic Haar graphs

Let $S$ be a subset of the cyclic group $\Z_n$. The cyclic Haar graph $H(\Z_n,S)$ is the bipartite graph with color classes $\Z_n^+$ and $\Z_n^-,$ and edges $\{x^+,y^-\},$ where $x,y \in \Z_n$ and $y - x \in S$. In this paper we give sufficient and necessary conditions for the isomorphism of two connected cyclic Haar graphs of valency 4.

math.CO↗

arXiv2012

Characterization of cyclic Schur groups

A finite group $G$ is called a Schur group, if any Schur ring over $G$ is the transitivity module of a permutation group on the set $G$ containing the regular subgroup of all right translations. It was proved by R. Pöschel (1974) that given a prime $p\ge 5$ a $p$-group is Schur if and only if it is cyclic. We prove that a cyclic group of order $n$ is a Schur group if and only if $n$ belongs to one of the following five (partially overlapped) families of integers: $p^k$, $pq^k$, $2pq^k$, $pqr$, $2pqr$ where $p,q,r$ are distinct primes, and $k\ge 0$ is an integer.

math.CO↗

arXiv2010

Automorphism groups of rational circulant graphs through the use of Schur rings

The paper concerns the automorphism groups of Cayley graphs over cyclic groups which have a rational spectrum (rational circulant graphs for short). With the aid of the techniques of Schur rings it is shown that the problem is equivalent to consider the automorphism groups of orthogonal group block structures of cyclic groups. Using this observation, the required groups are expressed in terms of generalized wreath products of symmetric groups.

math.CO↗