INTEGRAL HYPERGRAPHS OF THE DIRECT PRODUCT OF FANO PLANE AND LATIN SQUARES OF ORDER 3
Mulia Astuti and Zulfia Memi Mayasari

Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Bengkulu,
Jalan WR Supratman Kandang Limun Bengkulu, 38125

Abstract

The Hypergraph products have been a good way to construct a larger hypergraph from small ones. One of commonly studied hypergraph products is direct product. A hypergraph is called integral if all the eigenvalues of its adjacency matrix are integers. In this paper, We study two classes of hypergraphs, namely, Fano Plane and Latin Squares of Order 3. We show that two classes of hypergraphs are integral. Furthermore, we determine the direct product both of them. We prove that the hypergraph direct products preserve the integrality.

Keywords: Integral Hypergraphs, Direct Product, Fano Plane, and Latin Squares

Topic: Mathematics