Constructing directed strongly regular graphs by using semidirect products and semidihedral groups

Semih Piri; Oktay Olmez; Murat Şahin

doi:10.31801/cfsuasmas.1062880

Research Article

Year 2023, Volume: 72 Issue: 1, 22 - 31, 30.03.2023

Semih Piri , Oktay Olmez Murat Şahin

https://doi.org/10.31801/cfsuasmas.1062880

Abstract

References

Brouwer, A. E., Hobart, S., Parameters of directed strongly regular graphs. http://homepages.cwi.nl/ aeb/math/dsrg/dsrg.html
Duval, A., A directed graph version of strongly regular graphs, Journal of Combinatorial Theory Series A, 47 (1988), 71-100. https://doi.org/10.1016/0097-3165(88)90043-X
Duval, A., Iourinski, D., Semidirect product constructions of directed strongly regular graphs, Journal of Combinatorial Theory (A), 104 (2003), 157-167. https://doi.org/10.1016/S0097-3165(03)00141-9
Fiedler, F., Klin, M., Muzychuk, M., Small vertex-transitive directed strongly regular graphs, Discrete Mathematics, 255 (2002), 87-115. https://doi.org/10.1016/S0012-365X(01)00391-0
Fiedler, F., Klin, M., Pech, Ch., Directed Strongly Regular Graphs as Elements of Coherent Algebras, in: Denecke, K., Vogel, H.-J., (Eds.), General Algebra and Discrete Mathematics, Shaker Verlag, Aachen, 1999, 69-87.
Godsil, C. D., Hobart, S. A., Martin, W. J., Representations of directed strongly regular graphs, European J. Combin., 28(7) (2007), 1980-1993. https://doi.org/10.1016/j.ejc.2006.08.008
Hobart, S., Shaw, T., A note on a family of directed strongly regular graphs, European Journal of Combinatorics, 20 (1999), 819-820.
Jorgensen, L., Directed strongly regular graphs with $\mu=\lambda$, Discrete Mathematics, 231(1-3) (2001), 289-293.
Jorgensen, L., Non-existence of directed strongly regular graphs, Discrete Mathematics, 264 (2003), 111-126.
Klin, M., Munemasa, A., Muzychuk, M., Zieschang, P. H., Directed strongly regular graphs obtained from coherent algebras, Linear Algebra Appl., 377 (2004), 83-109.
Cameron, P. J., van Lint, J. H., Designs, Graphs, Codes and Their Links, Cambridge University Press, Cambridge, 1991.

Constructing directed strongly regular graphs by using semidirect products and semidihedral groups

Year 2023, Volume: 72 Issue: 1, 22 - 31, 30.03.2023

Semih Piri , Oktay Olmez Murat Şahin

https://doi.org/10.31801/cfsuasmas.1062880

Abstract

In this paper, directed strongly regular graphs (DSRGs) are constructed by using semidirect products. The orbit condition in [3] has been weakened and this gives rise to the construction of DSRGs. Moreover, a different construction is given for DSRG by using semidihedral groups.

Keywords

Directed strongly regular graphs, semidirect products, semidihedral groups, Cayley graphs

References

Brouwer, A. E., Hobart, S., Parameters of directed strongly regular graphs. http://homepages.cwi.nl/ aeb/math/dsrg/dsrg.html
Duval, A., A directed graph version of strongly regular graphs, Journal of Combinatorial Theory Series A, 47 (1988), 71-100. https://doi.org/10.1016/0097-3165(88)90043-X
Duval, A., Iourinski, D., Semidirect product constructions of directed strongly regular graphs, Journal of Combinatorial Theory (A), 104 (2003), 157-167. https://doi.org/10.1016/S0097-3165(03)00141-9
Fiedler, F., Klin, M., Muzychuk, M., Small vertex-transitive directed strongly regular graphs, Discrete Mathematics, 255 (2002), 87-115. https://doi.org/10.1016/S0012-365X(01)00391-0
Fiedler, F., Klin, M., Pech, Ch., Directed Strongly Regular Graphs as Elements of Coherent Algebras, in: Denecke, K., Vogel, H.-J., (Eds.), General Algebra and Discrete Mathematics, Shaker Verlag, Aachen, 1999, 69-87.
Godsil, C. D., Hobart, S. A., Martin, W. J., Representations of directed strongly regular graphs, European J. Combin., 28(7) (2007), 1980-1993. https://doi.org/10.1016/j.ejc.2006.08.008
Hobart, S., Shaw, T., A note on a family of directed strongly regular graphs, European Journal of Combinatorics, 20 (1999), 819-820.
Jorgensen, L., Directed strongly regular graphs with $\mu=\lambda$, Discrete Mathematics, 231(1-3) (2001), 289-293.
Jorgensen, L., Non-existence of directed strongly regular graphs, Discrete Mathematics, 264 (2003), 111-126.
Klin, M., Munemasa, A., Muzychuk, M., Zieschang, P. H., Directed strongly regular graphs obtained from coherent algebras, Linear Algebra Appl., 377 (2004), 83-109.
Cameron, P. J., van Lint, J. H., Designs, Graphs, Codes and Their Links, Cambridge University Press, Cambridge, 1991.

There are 11 citations in total.

Details

Primary Language	English
Subjects	Mathematical Sciences
Journal Section	Research Articles
Authors	Semih Piri 0000-0002-3978-0679 Oktay Olmez This is me 0000-0002-9130-0038 Murat Şahin 0000-0002-9480-0433
Publication Date	March 30, 2023
Submission Date	January 26, 2022
Acceptance Date	June 15, 2022
Published in Issue	Year 2023 Volume: 72 Issue: 1

Cite

APA	Piri, S., Olmez, O., & Şahin, M. (2023). Constructing directed strongly regular graphs by using semidirect products and semidihedral groups. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 72(1), 22-31. https://doi.org/10.31801/cfsuasmas.1062880
AMA	Piri S, Olmez O, Şahin M. Constructing directed strongly regular graphs by using semidirect products and semidihedral groups. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. March 2023;72(1):22-31. doi:10.31801/cfsuasmas.1062880
Chicago	Piri, Semih, Oktay Olmez, and Murat Şahin. “Constructing Directed Strongly Regular Graphs by Using Semidirect Products and Semidihedral Groups”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72, no. 1 (March 2023): 22-31. https://doi.org/10.31801/cfsuasmas.1062880.
EndNote	Piri S, Olmez O, Şahin M (March 1, 2023) Constructing directed strongly regular graphs by using semidirect products and semidihedral groups. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72 1 22–31.
IEEE	S. Piri, O. Olmez, and M. Şahin, “Constructing directed strongly regular graphs by using semidirect products and semidihedral groups”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 72, no. 1, pp. 22–31, 2023, doi: 10.31801/cfsuasmas.1062880.
ISNAD	Piri, Semih et al. “Constructing Directed Strongly Regular Graphs by Using Semidirect Products and Semidihedral Groups”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72/1 (March 2023), 22-31. https://doi.org/10.31801/cfsuasmas.1062880.
JAMA	Piri S, Olmez O, Şahin M. Constructing directed strongly regular graphs by using semidirect products and semidihedral groups. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2023;72:22–31.
MLA	Piri, Semih et al. “Constructing Directed Strongly Regular Graphs by Using Semidirect Products and Semidihedral Groups”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 72, no. 1, 2023, pp. 22-31, doi:10.31801/cfsuasmas.1062880.
Vancouver	Piri S, Olmez O, Şahin M. Constructing directed strongly regular graphs by using semidirect products and semidihedral groups. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2023;72(1):22-31.