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 2 n . 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 2 2n ; n∈Z ^+ .
Highlights
IntroductionA quaternary complex Hadamard matrix (Horadam, 2007) of order n is an n × n matrix H with T 1i}, ± i}
We have proposed an algorithm which can be used to generate strongly regular graphs from quaternary complex Hadamard matrices of order 2n for n ≥ 1
It can be seen that each block that are constructed by the operation Cm = cm cm for m = 2,4,... are symmetric
Summary
A quaternary complex Hadamard matrix (Horadam, 2007) of order n is an n × n matrix H with T 1i}, ± i}. I} such that H (H ) = nInIn nwhere I n is the entries from{± 1{{, ±1, identity matrix of order n. Following example gives the quaternary complex Hadamard matrix of order 2. Order 2n obtained by Sylvester’s construction (Wallis, 1975).
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