Normally Regular Digraphs

Seminar
Speaker
Leif Jørgensen (Aalborg U, Denmark)
Date
17/01/2016 - 15:30 - 14:00Add to Calendar 2016-01-17 14:00:00 2016-01-17 15:30:00 Normally Regular Digraphs A normally regular digraph with parameters (v,k,λ,μ) is a directed graph with adjacency matrix A satisfying the equation AAT=kI+λ(A+AT) +μ(J-I-A-AT).  I.e., the number of common out-neighbours of vertices x and y is k if x=y, μ if x and y are non-adjacent, λ if x and y are adjacent in one direction and 2λ-μ if they are adjacent in both directions. The adjacency matrix of a normally regular graph is normal, and all eigenvalues other than k are on one circle in the complex plane. This property characterizes normally regular digraphs. We consider constructions and structural characterizations and we also consider connections to association schemes, symmetric 2-designs, generalized difference sets, and partition of a projective plane into subplanes. Building 216, Room 201 אוניברסיטת בר-אילן - Department of Mathematics mathoffice@math.biu.ac.il Asia/Jerusalem public
Place
Building 216, Room 201
Abstract


A normally regular digraph with parameters (v,k,λ,μ) is a directed graph with adjacency matrix A satisfying the equation AAT=kI+λ(A+AT) +μ(J-I-A-AT).  I.e., the number of common out-neighbours of vertices x and y is k if x=y, μ if x and y are non-adjacent, λ if x and y are adjacent in one direction and 2λ-μ if they are adjacent in both directions.
The adjacency matrix of a normally regular graph is normal, and all eigenvalues other than k are on one circle in the complex plane. This property characterizes normally regular digraphs.
We consider constructions and structural characterizations and we also consider connections to association schemes, symmetric 2-designs, generalized difference sets, and partition of a projective plane into subplanes.

Last Updated Date : 13/01/2016