#### Research Articles

# Generation of strongly regular graphs from quaternary complex Hadamard matrices

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**Authors:**

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W. V. Nishadi ,

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University of Peradeniya, Peradeniya, LK

##### About W. V.

Department of Mathematics, Faculty of Science

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K. D. E. Dhananjaya,

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University of Peradeniya, Peradeniya, LK

##### About K. D. E.

Department of Mathematics, Faculty of Science

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A. A. I. Perera,

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University of Peradeniya, Peradeniya, LK

##### About A. A. I.

Department of Mathematics, Faculty of Science

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P. Gunathilake

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University of Peradeniya, Peradeniya, LK

##### About P.

Department of Statistics and Computer Science, Faculty of Science

## 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^{^+}.
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How to Cite:
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Nishadi, W. V., Dhananjaya, K. D. E., Perera, A. A. I., & Gunathilake, P. (2018). Generation of strongly regular graphs from quaternary complex Hadamard matrices. *Ceylon Journal of Science*, *47*(1), 65–68. DOI: http://doi.org/10.4038/cjs.v47i1.7488
Published on 27 Mar 2018.

Peer Reviewed

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