Directed strongly regular Cayley graphs on dihedral groups
作者：
Highlights：
• This is a further development of previous result, can refer He, Zhang, The application of representation theory in directed strongly regular graphs, Journal of Combinatorial Theory, Series A 161 (2019) 508–536. We have found more information about the directed strongly regular Cayley graph on dihedral groups Dpα, where p is a prime and α ≥ 1 is a positive integer.
• The characterization of directed strongly regular dihedrant Dih(p;X;Y) has been achieved. For the case of prime power, the proof is considerably difficult from the original case. We overcome the difficulty by technical use of character theory of finite abelian groups.
• The fact that DSRG have integral eigenvalues is a key in the argument. I think our results are nontrivial and interesting.
摘要
•This is a further development of previous result, can refer He, Zhang, The application of representation theory in directed strongly regular graphs, Journal of Combinatorial Theory, Series A 161 (2019) 508–536. We have found more information about the directed strongly regular Cayley graph on dihedral groups Dpα, where p is a prime and α ≥ 1 is a positive integer.•The characterization of directed strongly regular dihedrant Dih(p;X;Y) has been achieved. For the case of prime power, the proof is considerably difficult from the original case. We overcome the difficulty by technical use of character theory of finite abelian groups.•The fact that DSRG have integral eigenvalues is a key in the argument. I think our results are nontrivial and interesting.
论文关键词：Directed strongly regular graph,Cayley graph,Dihedral group,Character theory,Fourier transformation
论文评审过程：Received 15 February 2020, Revised 13 August 2020, Accepted 15 August 2020, Available online 12 September 2020, Version of Record 12 September 2020.
论文官网地址：https://doi.org/10.1016/j.amc.2020.125651
