Refined Lower Bounds for the Laplacian Estrada Index of Connected Graphs via the Two Largest Degrees

Hamidreza Bamdad, Alireza Vahidi and Akram Mahmoodi

Journal of Mathematics, 2026, vol. 2026, 1-5

Abstract: Let G be a graph with n vertices and Laplacian eigenvalues μ1,μ2,…,μn. The Laplacian Estrada index of G is defined as LEEG=eμ1+⋯+eμn. In this paper, using the Karush–Kuhn–Tucker optimization framework under inequality constraints, we establish new lower bounds for LEEG in terms of the two largest degrees of G. Specifically, if G is a connected graph with n≥3 vertices, m edges, and degree sequence d1≥d2≥⋯≥dn, then LEEG≥1+ed1+1+ed2+n−3e2m−d1−d2−1/n−3 if d3+⋯+dn≤n−3d2 and LEEG≥1+ed1+1+n−2ed2 otherwise. These inequalities improve previously known results on the Laplacian Estrada index.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:8890484

DOI: 10.1155/jom/8890484

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