Eigen Spectrum of k-uniform Cyclic Hypergraphs

Abstract

Hypergraphs are generalization of graphs, introduced by Berge . In an ordinary graph, an edge connects exactly two vertices, where as in hypergraphs a hyperedge is a subset of the vertex set . Hypergraphs have applications in the field of Computer Science, Machine learning, Neural networks etc. In this paper, we derive a formula to obtain eigen spectrum of k-uniform cyclic hypergraphs C^k_n
. There after we apply the result on cyclic graph C_n, dual hypergraph (C^k_n)∗ of C^k_n, intersection graph of C^k_n and cartesian product hypergraphof K2 with C^k_n . Highlight of this work is that we got a general result for the eigen spectrum of the cyclic hypergraph
C^k_n which coincides with that of the cyclic graph C_n when k = 2