Laplacian Estrada index of trees
Aleksandar Ilic, Bo Zhou

TL;DR
This paper investigates the Laplacian Estrada index of trees, establishing extremal values for paths and stars, and identifying the second maximal tree, thereby advancing understanding of spectral graph invariants.
Contribution
It proves extremal properties of the Laplacian Estrada index for trees and identifies the second maximal tree, using a novel connection with the Estrada index of line graphs.
Findings
Path $P_n$ has the minimal Laplacian Estrada index among trees.
Star $S_n$ has the maximal Laplacian Estrada index among trees.
The unique tree with the second maximal Laplacian Estrada index is characterized.
Abstract
Let be a simple graph with vertices and let be the eigenvalues of its Laplacian matrix. The Laplacian Estrada index of a graph is defined as . Using the recent connection between Estrada index of a line graph and Laplacian Estrada index, we prove that the path has minimal, while the star has maximal among trees on vertices. In addition, we find the unique tree with the second maximal Laplacian Estrada index.
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Taxonomy
TopicsGraph theory and applications · Computational Drug Discovery Methods · Advanced Graph Theory Research
