Back to Search
Start Over
The trace and Estrada index of uniform hypergraphs with cut vertices
- Source :
- Linear Algebra and its Applications, Volume 660, 1 March 2023, Pages 89-117
- Publication Year :
- 2022
-
Abstract
- Let $\mathcal{H}$ be an $m$-uniform hypergraph, and let $\mathcal{A}(\mathcal{H})$ be the adjacency tensor of $\mathcal{H}$ which can be viewed as a system of homogeneous polynomials of degree $m-1$. Morozov and Shakirov generalized the traces of linear systems to nonlinear homogeneous polynomial systems and obtained explicit formulas for multidimensional resultants. Sun, Zhou and Bu introduced the Estrada index of uniform hypergraphs which is closely related to the traces of their adjacency tensors. In this paper we give formulas for the traces of $\mathcal{A}(\mathcal{H})$ when $\mathcal{H}$ contains cut vertices, and obtain results on the traces and Estrada index when $\mathcal{H}$ is perturbed under local changes. We prove that among all hypertrees with fixed number of edges, the hyperpath is the unique one with minimum Estrada index and the hyperstar is the unique one with maximum Estrada index.
- Subjects :
- Mathematics - Combinatorics
Primary 05C65, 15A69, , Secondary 13P15, 14M99
Subjects
Details
- Database :
- arXiv
- Journal :
- Linear Algebra and its Applications, Volume 660, 1 March 2023, Pages 89-117
- Publication Type :
- Report
- Accession number :
- edsarx.2205.15502
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1016/j.laa.2022.12.006