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The trace of uniform hypergraphs with application to Estrada index

Authors :
Fan, Yi-Zheng
Zheng, Jian
Yang, Ya
Publication Year :
2022
Publisher :
arXiv, 2022.

Abstract

In this paper we investigate the traces of the adjacency tensor of hypergraphs (simply called the traces of hypergraphs). We give new expressions for the traces of hypertrees and linear unicyclic hypergraphs by the weight function assigned to their connected sub-hypergraphs, and provide some perturbation results for the traces of a hypergraph with cut vertices. As applications we determine the unique hypertree with maximum Estrada index among all hypertrees with fixed number of edges and perfect matchings, and the unique unicyclic hypergraph with maximum Estrada index among all unicyclic hypergraph with fixed number of edges and girth $3$.

Details

Database :
OpenAIRE
Accession number :
edsair.doi.dedup.....8eb10abe3febc949d48be57aeb5b3929
Full Text :
https://doi.org/10.48550/arxiv.2210.03311