Isomorphisms of bi-Cayley graphs on Dihedral groups-Reference-Cited by-同舟云学术

Isomorphisms of bi-Cayley graphs on Dihedral groups

Published:2020-06-15 Issue:04 Volume:12 Page:2050051
ISSN:1793-8309
Container-title:Discrete Mathematics, Algorithms and Applications
language:en
Short-container-title:Discrete Math. Algorithm. Appl.

Author:

Arezoomand Majid¹,Behmaram Afshin²,Ghasemi Mohsen³,Raeighasht Parivash⁴

Affiliation:

1. University of Larestan, Larestan, Iran

2. Faculty of mathematical sciences, University of Tabriz, Tabriz, Iran

3. Department of Mathematics, Urmia University, Urmia 57135, Iran

4. Faculty of Mathematics, University of Tabriz, Tabriz, Iran

Abstract

For a group [Formula: see text] and a subset [Formula: see text] of [Formula: see text] the bi-Cayley graph BCay[Formula: see text] of [Formula: see text] with respect to [Formula: see text] is the bipartite graph with vertex set [Formula: see text] and edge set [Formula: see text]. A bi-Cayley graph BCay[Formula: see text] is called a BCI-graph if for any bi-Cayley graph BCay[Formula: see text], [Formula: see text] implies that [Formula: see text] for some [Formula: see text] and [Formula: see text]. A group [Formula: see text] is called a [Formula: see text]-BCI-group if all bi-Cayley graphs of [Formula: see text] with valency at most [Formula: see text] are BCI-graphs. In this paper, we characterize the [Formula: see text]-BCI dihedral groups for [Formula: see text]. Also, we show that the dihedral group [Formula: see text] ([Formula: see text] is prime) is a [Formula: see text]-BCI-group.

Publisher

World Scientific Pub Co Pte Lt

Subject

Discrete Mathematics and Combinatorics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793830920500512

Reference13 articles.

1. On the Characteristic Polynomial of $n$-Cayley Digraphs

2. A classification of nonabelian simple 3-BCI-groups