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Isomorphisms of bi-Cayley graphs on Dihedral groups.
- Source :
- Discrete Mathematics, Algorithms & Applications; Aug2020, Vol. 12 Issue 04, pN.PAG-N.PAG, 9p
- Publication Year :
- 2020
-
Abstract
- For a group G and a subset S of G the bi-Cayley graph BCay (G , S) of G with respect to S is the bipartite graph with vertex set G × { 0 , 1 } and edge set { { (x , 0) , (s x , 1) } | x ∈ G , s ∈ S }. A bi-Cayley graph BCay (G , S) is called a BCI-graph if for any bi-Cayley graph BCay (G , T) , BCay (G , S) ≅ BCay (G , T) implies that T = g S α for some g ∈ G and α ∈ Aut (G). A group G is called a m -BCI-group if all bi-Cayley graphs of G with valency at most m are BCI-graphs. In this paper, we characterize the m -BCI dihedral groups for m ≤ 3. Also, we show that the dihedral group D 2 p (p is prime) is a 4 -BCI-group. [ABSTRACT FROM AUTHOR]
- Subjects :
- ISOMORPHISM (Mathematics)
CAYLEY graphs
BIPARTITE graphs
VALENCE (Chemistry)
Subjects
Details
- Language :
- English
- ISSN :
- 17938309
- Volume :
- 12
- Issue :
- 04
- Database :
- Complementary Index
- Journal :
- Discrete Mathematics, Algorithms & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 145107117
- Full Text :
- https://doi.org/10.1142/S1793830920500512