Research Projects

In [3, 2021],, the author defined an adjacency matrix and corresponding Laplacian matrix for a hypergraph. In the same article the author supplied diiferent bounds for the second smalles and the largest eigenvalue (spectral )of the adjacency ( Laplacian) matrix in terms of diameter, chromatic number, weak connectivity etc. We have already mentioned that in [3], the author supplied diiferent bounds for the second smalles and largest eigenvalue of the adjacency ( Laplacian) matrix in terms of diameter, chromatic number, weak connectivity etc. This is the only article available in this direction. The spectrum of these two matricrs are yet to explore. In this project we want to explore the spectrum of this Lapalcian matrix of hypergraphs. For example, we know that the spectral radius of a graph G of order n is atmost n and equality holds if and only if the complement graph of G is disconnected. It is clear that graph is a two uniform hypergraph. It is natural to ask whether this type result can be extended for k uniform hypergraphs or not. We explore different properties of spectrum of Laplacian matrix associated with a hypergraphs.

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