Singular graphs with dihedral group action

Ali Sltan Ali AL-Tarimshawy; J. Siemons

doi:10.1016/j.disc.2020.112119

Singular graphs with dihedral group action

Ali Sltan Ali AL-Tarimshawy, J. Siemons

Algebra, Number Theory, Logic, and Representations (ANTLR)

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

4 Citations (SciVal)

Abstract

Let Γ be a simple undirected graph on a finite vertex set and let A be its adjacency matrix. Then Γ is singular if A is singular. The problem of characterizing singular graphs is easy to state but very difficult to resolve in any generality. In this paper we investigate the singularity of graphs for which the dihedral group acts transitively on vertices as a group of automorphisms.

Original language	English
Article number	112119
Journal	Discrete Mathematics
Volume	344
Issue number	1
Early online date	15 Oct 2020
DOIs	https://doi.org/10.1016/j.disc.2020.112119
Publication status	Published - Jan 2021

Keywords

Dihedral action
Graph spectrum
Singular graph

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10.1016/j.disc.2020.112119Licence: Other

Cite this

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title = "Singular graphs with dihedral group action",

abstract = "Let Γ be a simple undirected graph on a finite vertex set and let A be its adjacency matrix. Then Γ is singular if A is singular. The problem of characterizing singular graphs is easy to state but very difficult to resolve in any generality. In this paper we investigate the singularity of graphs for which the dihedral group acts transitively on vertices as a group of automorphisms.",

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AB - Let Γ be a simple undirected graph on a finite vertex set and let A be its adjacency matrix. Then Γ is singular if A is singular. The problem of characterizing singular graphs is easy to state but very difficult to resolve in any generality. In this paper we investigate the singularity of graphs for which the dihedral group acts transitively on vertices as a group of automorphisms.

KW - Dihedral action

KW - Graph spectrum

KW - Singular graph

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JO - Discrete Mathematics

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Singular graphs with dihedral group action

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Johannes Siemons

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Singular graphs with dihedral group action

Abstract

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Johannes Siemons

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