Generation of strongly regular graphs from quaternary complex Hadamard matrices

Abstract

A strongly regular graph with parameters (v, k, μ, λ) is a regular graph G with v vertices and k degree in which every two adjacent vertices have λ common neighbors and every two non-adjacent vertices have μ common neighbors. In this paper, we propose an algorithm which can be used to construct strongly regular graphs using quaternary complex Hadamard matrices. The order of the strongly regular graph generated by a quaternary complex Hadamard matrix of order n is 2n. The proposed algorithm has been illustrated by generating a strongly regular graph of order 4 using quaternary complex Hadamard matrix of order 2. Further, higher order strongly regular graphs were tested using Java program. This algorithm could be used to construct strongly regular graphs of order 22n; n∈Z^+.

Keywords

• tensor product, simple graphs, k- regular graphs, strongly regular graphs, adjacency matrix, latin squares, cyclic shifting method