On the p-Rank of the Adjacency Matrices of Strongly Regular Graphs

Authors:
A. E. Brouwer;C. A. Van Eijl
Affiliations:
Dept. of Math., Eindhoven Univ. of Technology, Eindhoven, Netherlands;Dept. of Math., Eindhoven Univ. of Technology, Eindhoven, Netherlands
Venue:
Journal of Algebraic Combinatorics: An International Journal
Year:
1992

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Abstract

Let Γ be a strongly regular graph with adjacency matrix A. Let I be the identity matrix, and J the all-1 matrix. Let p be a prime. Our aim is to study the p-rank (that is, the rank over \Bbb {F}_p, the finite field with p elements) of the matrices M = aA + bJ + cI for integral a, b, c. This note is based on van Eijl [8].