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A beautiful conjecture by Murty and Simon, says that every diameter-2-critical graph of order $n$ has at most $\\lfloor n^2/4\\rfloor$ edges and equality holds only for $K_{\\lceil n/2 \\rceil,\\lfloor n/2 \\rfloor }$. Haynes et al. proved that the conjecture is true for $\\Delta\\geq 0.7n$. They also proved that for $n>2000$, if $\\Delta \\geq 0.6789n$ then the conjecture is true. We will improve this bound by showing that the conjecture is true for every $n$ if $\\Delta\\geq\\ 0.676n"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1610.00360","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-10-02T22:05:14Z","cross_cats_sorted":[],"title_canon_sha256":"62f99f28f4032e1d34bc2ec9ee988e33b0ca465e752abbc0151812d05d5be927","abstract_canon_sha256":"09559d29e930049ea3845a33d00060785abb5f8bb5c40222ff1bf5d9c9954ff1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:02:51.644246Z","signature_b64":"3qkqsKq0UcewkUgOR04GoAOg3LEgN//jK4gfVTk/D/qK2Yw5+Ex2vmrA+yltNj/skrKoZm3OXjxfrDhJvjmJDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c600d1a36773d411d2f8a8e7c983e1c68da7e77d5a0a807eaf0c82f0bf482d7a","last_reissued_at":"2026-05-18T01:02:51.643802Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:02:51.643802Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Improving the Bounds On Murty_Simon Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Afrouz Jabalameli, Amin behjati, MohammadMahdi Shokri, Mohsen Ferdosi, Morteza Saghafian, Sorush Bahariyan","submitted_at":"2016-10-02T22:05:14Z","abstract_excerpt":"A graph is said to be diameter-$k$-critical if its diameter is $k$ and removal of any of its edges increases its diameter. 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