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The \\textit{inertia} of $G_w$ is the triple $In(G_w)=\\big(i_+(G_w),i_-(G_w), $ $ i_0(G_w)\\big)$, where $i_+(G_w),i_-(G_w),i_0(G_w)$ are the number of the positive, negative and zero eigenvalues of the adjacency matrix $A(G_w)$ of $G_w$ including their multiplicities, respectively. $i_+(G_w)$, $i_-(G_w)$ is called the \\textit{positive, negative index of inertia} of $G_w$, respectively. In this paper we present a lower bound for the positive, negative index of weighted unicyclic graphs of order $n$ with fixed girth and characterize all weighted unicyclic graphs att"},"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":"1307.0059","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-06-29T01:24:25Z","cross_cats_sorted":[],"title_canon_sha256":"81e3ee61683595ddc10603e7b763a05549db7e86aa5e8721232f2f46d0fe15b8","abstract_canon_sha256":"67534310b8c0baf1bb403bebb04be18bb424c5df479d590e51fdf383b027e169"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:19:34.361871Z","signature_b64":"LmLdbYjKpergXfteUwUV9dmC26ePQxpf5ZrWZwD30AOIKT9tBx6xHojAEuVqRM4HBCAgo/mkfAR/zGFc5xfMDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"273a4c849dd6ebf693153b30f78c7626249008f8531dfa503e7262f1763e0571","last_reissued_at":"2026-05-18T03:19:34.361513Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:19:34.361513Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The inertia of weighted unicyclic graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Guihai Yu, Lihua Feng, Xiao-Dong Zhang","submitted_at":"2013-06-29T01:24:25Z","abstract_excerpt":"Let $G_w$ be a weighted graph. The \\textit{inertia} of $G_w$ is the triple $In(G_w)=\\big(i_+(G_w),i_-(G_w), $ $ i_0(G_w)\\big)$, where $i_+(G_w),i_-(G_w),i_0(G_w)$ are the number of the positive, negative and zero eigenvalues of the adjacency matrix $A(G_w)$ of $G_w$ including their multiplicities, respectively. $i_+(G_w)$, $i_-(G_w)$ is called the \\textit{positive, negative index of inertia} of $G_w$, respectively. 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