A new construction of antipodal distance regular covers of complete graphs through the use of Godsil-Hensel matrices

Mikhail Klin; Christian Pech

A new construction of antipodal distance regular covers of complete graphs through the use of Godsil-Hensel matrices

Mikhail Klin, Christian Pech

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

Abstract

New constructions of regular distance regular antipodal covers (in the sense of Godsil- Hensel) of complete graphs K_n are presented. The main source of these constructions are skew generalized Hadamard matrices. It is described how to produce such a matrix of order n² over a group T from an arbitrary given generalized Hadamard matrix of order n over the same group T. Further, a new regular cover of K ₄₅on 135 vertices is produced with the aid of a decoration of the alternating group A₆.

Original language	English
Pages (from-to)	205-243
Number of pages	39
Journal	Ars Mathematica Contemporanea
Volume	4
Issue number	2
State	Published - 13 Oct 2011

Keywords

Antipodal graph
Association scheme
Automorphism group
Conference matrix
Distance regular cover
Foster graph
Generalized Hadamard matrix
Godsil-Hensel matrix
Group ring
Mathieu group
Payne's doily
Resolvable transversal design
Schur multiplier
Semibiplane
Taylor graph
Tutte's 8-cage
Two-graph
Wielandt's 2-closure

ASJC Scopus subject areas

Theoretical Computer Science
Algebra and Number Theory
Geometry and Topology
Discrete Mathematics and Combinatorics

Cite this

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title = "A new construction of antipodal distance regular covers of complete graphs through the use of Godsil-Hensel matrices",

abstract = "New constructions of regular distance regular antipodal covers (in the sense of Godsil- Hensel) of complete graphs Kn are presented. The main source of these constructions are skew generalized Hadamard matrices. It is described how to produce such a matrix of order n2 over a group T from an arbitrary given generalized Hadamard matrix of order n over the same group T. Further, a new regular cover of K 45on 135 vertices is produced with the aid of a decoration of the alternating group A6.",

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N2 - New constructions of regular distance regular antipodal covers (in the sense of Godsil- Hensel) of complete graphs Kn are presented. The main source of these constructions are skew generalized Hadamard matrices. It is described how to produce such a matrix of order n2 over a group T from an arbitrary given generalized Hadamard matrix of order n over the same group T. Further, a new regular cover of K 45on 135 vertices is produced with the aid of a decoration of the alternating group A6.

AB - New constructions of regular distance regular antipodal covers (in the sense of Godsil- Hensel) of complete graphs Kn are presented. The main source of these constructions are skew generalized Hadamard matrices. It is described how to produce such a matrix of order n2 over a group T from an arbitrary given generalized Hadamard matrix of order n over the same group T. Further, a new regular cover of K 45on 135 vertices is produced with the aid of a decoration of the alternating group A6.

KW - Antipodal graph

KW - Association scheme

KW - Automorphism group

KW - Conference matrix

KW - Distance regular cover

KW - Foster graph

KW - Generalized Hadamard matrix

KW - Godsil-Hensel matrix

KW - Group ring

KW - Mathieu group

KW - Payne's doily

KW - Resolvable transversal design

KW - Schur multiplier

KW - Semibiplane

KW - Taylor graph

KW - Tutte's 8-cage

KW - Two-graph

KW - Wielandt's 2-closure

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M3 - Article

AN - SCOPUS:80053654996

SN - 1855-3966

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JO - Ars Mathematica Contemporanea

JF - Ars Mathematica Contemporanea

IS - 2

ER -

A new construction of antipodal distance regular covers of complete graphs through the use of Godsil-Hensel matrices

Abstract

Keywords

ASJC Scopus subject areas

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