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A directed graph version of strongly regular graphs

Duval, Art M. (1988) A directed graph version of strongly regular graphs. Journal of Combinatorial Theory. Series A, 47 (1). pp. 71-100. ISSN 0097-3165. doi:10.1016/0097-3165(88)90043-X.

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We study a directed graph version of strongly regular graphs whose adjacency matrices satisfy A^2 + (μ − λ)A − (t − μ)I = μJ, and AJ = JA = kJ. We prove existence (by construction), nonexistence, and necessary conditions, and construct homomorphisms for several families of parameter sets.

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Additional Information:© 1988 Published by Elsevier. Received 17 June 1986. Dedicated to the memory of Herbert J. Ryser. Work on this paper done partially while the author was supported by a Summer Undergraduate Research Fellowship at the California Institute of Technology, and partially as a Senior Thesis at the California Institute of Technology. I acknowledge the assistance of Professor Herbert J. Ryser, who led me to this problem, Professors Richard M. Wilson and Richard A. Brualdi, who provided valuable assistance, and the referee, who suggested many improvements.
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Caltech Summer Undergraduate Research Fellowship (SURF)UNSPECIFIED
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Record Number:CaltechAUTHORS:20180720-163236767
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Official Citation:Art M Duval, A directed graph version of strongly regular graphs, Journal of Combinatorial Theory, Series A, Volume 47, Issue 1, 1988, Pages 71-100, ISSN 0097-3165, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:88109
Deposited By: George Porter
Deposited On:23 Jul 2018 22:08
Last Modified:16 Nov 2021 00:24

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