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In this paper, we present the bounds for $p(G)$ and $n(G)$ as follows:\n  $$m(G)-c(G)\\leq p(G)\\leq m(G)+c(G), \\ m(G)-c(G)\\leq n(G)\\leq m(G)+c(G),$$\n  where $m(G)$ and $c(G)$ are respectively the matching number and the cyclomatic number of $G$. Furthermore, we characterize the graphs which attain the upper bounds or th"},"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":"1409.5328","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-09-18T15:08:11Z","cross_cats_sorted":[],"title_canon_sha256":"0cc84dca811b7ac5167711edc7563b5b4bd9328931f3fbe2cd853ab6a2358ffc","abstract_canon_sha256":"3fd7cc629aba44d8a95b623a1b0185ab74b58bcdb16835701e31935be6adf66a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:55.920058Z","signature_b64":"O7aOW3gR0gGhCos7M7GJHv3JXL7HtKIyj9qsACQuDu3yu73S9cvFFCp1CoWEe20FhZ43bOKJhdGkAzQa1euQDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5bc4c6c78514b902554978ff160894a169928d4cdbcfa7925d3a339a4bbfa5a2","last_reissued_at":"2026-05-18T00:35:55.919647Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:55.919647Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bounds for the positive or negative inertia index of a graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Long Wang, Yi-Zheng Fan","submitted_at":"2014-09-18T15:08:11Z","abstract_excerpt":"Let $G$ be a graph and let $A(G)$ be adjacency matrix of $G$.The positive inertia index (respectively, the negative inertia index) of $G$, denoted by $p(G)$ (respectively, $n(G)$), is defined to be the number of positive eigenvalues (respectively, negative eigenvalues) of $A(G)$. In this paper, we present the bounds for $p(G)$ and $n(G)$ as follows:\n  $$m(G)-c(G)\\leq p(G)\\leq m(G)+c(G), \\ m(G)-c(G)\\leq n(G)\\leq m(G)+c(G),$$\n  where $m(G)$ and $c(G)$ are respectively the matching number and the cyclomatic number of $G$. 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