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Using the recent connection between Estrada index of a line graph and Laplacian Estrada index, we prove that the path $P_n$ has minimal, while the star $S_n$ has maximal $LEE$ among trees on $n$ vertices. In addition, we find the unique tree with the second maximal Laplacian Estrada index."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1106.3041","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-06-15T17:59:56Z","cross_cats_sorted":[],"title_canon_sha256":"5903064c06f662403646d454ca6c99a092c022166463ee408f2dfa7a7475db8f","abstract_canon_sha256":"ddf1b1eeb804ed3182fb73dd0970640db0c0fd47a3bfc7b10492b815c0963055"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:19:55.128462Z","signature_b64":"qeoUbqw6A2Mhb5nRAChg5AbfGUvXpEZAyY3ri75nsaAypFGuTSZilcde943HgU5QYoH62cP3kWRVk/LvJi10Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1a3ad255a1c4a7e444bdf4b9f3b0e68f24bc692c2a0d6dbc8d8b9a8591b23981","last_reissued_at":"2026-05-18T04:19:55.127797Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:19:55.127797Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Laplacian Estrada index of trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Aleksandar Ilic, Bo Zhou","submitted_at":"2011-06-15T17:59:56Z","abstract_excerpt":"Let $G$ be a simple graph with $n$ vertices and let $\\mu_1 \\geqslant \\mu_2 \\geqslant...\\geqslant \\mu_{n - 1} \\geqslant \\mu_n = 0$ be the eigenvalues of its Laplacian matrix. The Laplacian Estrada index of a graph $G$ is defined as $LEE (G) = \\sum\\limits_{i = 1}^n e^{\\mu_i}$. Using the recent connection between Estrada index of a line graph and Laplacian Estrada index, we prove that the path $P_n$ has minimal, while the star $S_n$ has maximal $LEE$ among trees on $n$ vertices. 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