Abstract
It is known that there is a close relation between directed strongly regular graphs and partial sum families. In this short note, we construct some partial sum families from known directed strongly regular graphs. As a byproduct, we give a partial answer to a question posed by Martínez in [4].
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
A. Araluze, I. Kovács, K. Kutnar, L. Martínez, D. Marušič, Partial sum quadruples and bi-Abelian digraphs. J. Combin. Theory Ser. A 119, 1811–1831 (2012)
A.M. Duval, A directed graph version of strongly regular graphs. J. Combin. Theory Ser. A 47, 71–100 (1988)
GAP - Groups, Algorithms, Programming - a System for Computational Discrete Algebra, https://www.gap-system.org
L. Martínez, Strongly regular \(m\)-Cayley circulant graphs and digraphs. Ars Mathem. Contemporanea 8, 195–213 (2015)
L. Martínez, A. Araluze, New tools for construction of directed strongly regular digraphs: difference digraphs and partial sum families. J. Combin. Theory Ser. B 100, 720–728 (2010)
O. Olmez, S.Y. Song, Some families of directed strongly regular graphs obtained from certain finite incidence structures. Graphs Combin. 30, 1529–1549 (2014)
Acknowledgements
The author gratefully acknowledges the contribution of the Scientific Grant Agency of Slovak Republic under the grant VEGA 1/0988/16 and the contribution of the Slovak Research and Development Agency under the projects APVV-0136-12 and APVV-0220-15.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Gyürki, Š. (2020). A Note on a Problem of L. Martínez on Almost-Uniform Partial Sum Families. In: Jones, G., Ponomarenko, I., Širáň, J. (eds) Isomorphisms, Symmetry and Computations in Algebraic Graph Theory. WAGT 2016. Springer Proceedings in Mathematics & Statistics, vol 305. Springer, Cham. https://doi.org/10.1007/978-3-030-32808-5_3
Download citation
DOI: https://doi.org/10.1007/978-3-030-32808-5_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-32807-8
Online ISBN: 978-3-030-32808-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)