Equitable Partition Theorem of Tensors and Spectrum of Generalized Power Hypergraphs

TL;DR

This paper extends equitable partition theory from graphs to hypergraphs using tensors, establishing relations between eigenvalues of tensors and their quotients, and applies these results to analyze generalized power hypergraphs.

Contribution

It introduces an equitable partition theorem for tensors, extending graph theory concepts to hypergraphs and deriving properties of eigenvalues for generalized power hypergraphs.

Findings

Established relations between eigenvalues of tensors and their quotients.

Extended equitable partition concepts from graphs to hypergraphs.

Derived properties and eigenvalues of generalized power hypergraphs.

Abstract

In this paper, we present an equitable partition theorem of tensors, which gives the relations between $H$-eigenvalues of a tensor and its quotient equitable tensor and extends the equitable partitions of graphs to hypergraphs. Furthermore, with the aid of it, some properties and $H$-eigenvalues of the generalized power hypergraphs are obtained, which extends some known results, including some results of Yuan, Qi and Shao.