On the Maximum Estrada Index of 3-Uniform Linear Hypertrees

Faxu Li,Haixing Zhao,Feng Hu,Liang Wei,Jinde Cao

doi:10.1155/2014/637865

Abstract

For a simple hypergraph H on n vertices, its Estrada index is defined as , where λ 1, λ 2,…, λ n are the eigenvalues of its adjacency matrix. In this paper, we determine the unique 3-uniform linear hypertree with the maximum Estrada index.

Highlights

IntroductionThe hypergraph H is called linear if two hyperedges intersect in one vertex at most and h-uniform if |Ei| = h for each Ei in E, i = 1, 2,
Let G = (V, E) be a simple graph, and let n and m be the number of vertices and the number of edges of G, respectively
For more results on the Estrada index, the readers are referred to recent papers [16,17,18,19]

Summary

Introduction

The hypergraph H is called linear if two hyperedges intersect in one vertex at most and h-uniform if |Ei| = h for each Ei in E, i = 1, 2, . Let A(H) denote a square symmetric matrix in which the diagonal elements aij are zero, and other elements aij represent the number of hyperedges containing both vertices Vi and Vj (for undirected hypergraphs, aij = aji). The subhypergraph centrality of a hypergraph H, firstly put forward by Estrada and Rodrıguez-Velazquez in 2006, is defined as [21]. Our main goal is to investigate the Estrada index of 3-uniform linear hypertrees. We determine the unique 3-uniform linear hypertree with the maximum Estrada index among the set of 3-uniform linear hypertrees

Preliminaries

Maximum Estrada Index of 3-Uniform Linear Hypertrees