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

Semih Piri , Oktay Olmez Murat Şahin

https://doi.org/10.31801/cfsuasmas.1062880
https://izlik.org/JA65MX86HB

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
https://izlik.org/JA65MX86HB

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 Article
Authors

Semih Piri 0000-0002-3978-0679

Oktay Olmez This is me 0000-0002-9130-0038

Murat Şahin 0000-0002-9480-0433

Submission Date January 26, 2022
Acceptance Date June 15, 2022
Publication Date March 30, 2023
DOI https://doi.org/10.31801/cfsuasmas.1062880
IZ https://izlik.org/JA65MX86HB
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 1.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. doi:10.31801/cfsuasmas.1062880
Chicago Piri, Semih, Oktay Olmez, and Murat Şahin. 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.
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 [1]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, Mar. 2023, doi: 10.31801/cfsuasmas.1062880.
ISNAD Piri, Semih - Olmez, Oktay - Şahin, Murat. “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 1, 2023): 22-31. https://doi.org/10.31801/cfsuasmas.1062880.
JAMA 1.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, Mar. 2023, pp. 22-31, doi:10.31801/cfsuasmas.1062880.
Vancouver 1.Semih Piri, Oktay Olmez, Murat Şahin. Constructing directed strongly regular graphs by using semidirect products and semidihedral groups. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2023 Mar. 1;72(1):22-31. doi:10.31801/cfsuasmas.1062880

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