We introduce a special kind of partial sum families, which we call equisizable partial sum families, that can be used to obtain directed strongly regular graphs admitting a semiregular group of automorphisms. We give a construction of an infinite family of equisizable partial sum families depending on two parameters that produce directed strongly regular graphs with new parameters. We also determine the automorphisms group of the associated directed strongly regular graphs in terms of the parameters.
Luis Martínez was supported by the Basque Government Grant IT974-16 and by the UPV/EHU and Basque Center of Applied Mathematics, grant US18/21. The work of István Kovács was supported in part by the Slovenian Research Agency (Research Program P1-0285 and Research Projects N1-0032, N1-0038, N1-0062, J1-6720, J1-7051, J1-9108). The work of Klavdija Kutnar was supported in part by the Slovenian Research Agency (Research Program P1-0285 and Research Projects N1-0032, N1-0038, J1-6720, J1-6743, J1-7051, J1-9110), in part by WoodWisdom-Net\(+\), W\(^3\)B, and in part by NSFC Project 11561021. The work of Dragan Marušič was supported in part by the Slovenian Research Agency (I0-0035, Research Program P1-0285 and Research Projects N1-0032, N1-0038, N1-0062, J1-5433, J1-6720, J1-7051, J1-9108) and in part by H2020 Teaming InnoRenew CoE (Grant No. 739574).
We would like to thank the anonymous referees for valuable comments and suggestions.