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[7] introduced Jaco Graphs (\\emph{order 1}). In this essay we present a recursive formula to determine the \\emph{independence number} $\\alpha(J_n(1)) = |\\Bbb I|$ with, $\\Bbb I = \\{v_{i,j}| v_1 = v_{1,1} \\in \\Bbb I$ and $v_i = v_{i,j} =v_{(d^+(v_{m, (j-1)}) + m +1)}\\}.$ We also prove that for the Jaco Graph, $J_n(1), n \\in \\Bbb N$ with the prime Jaconian vertex $v_i$ the chromatic number, $\\chi(J_n(1))$ is given by: \\begin{equation*} \\chi(J_n(1)) \\begin{cases} = (n-i) + 1, &\\text{if and only if the edge $v_iv_n$ exists,}\\\\ \\\\ = n-i &\\text{otherwise.} \\end{cases} \\end{equation*} We fu","authors_text":"Johan Kok, Susanth C","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CO","submitted_at":"2014-10-30T11:14:30Z","title":"Contemplating some invariants of the Jaco Graph, $J_n(1), n \\in \\Bbb N$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.8328","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:8333e74af05d9c21f35974e423cea721aa1c1eb3969ab26d31fbb1c28ba295d0","target":"record","created_at":"2026-05-18T02:39:00Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"e51be8dcebdcc32d115252646ecb29395b7656407a3aac6096e709b588b79179","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CO","submitted_at":"2014-10-30T11:14:30Z","title_canon_sha256":"ffbc931740ab19b5c3293a18037bd4fd8636a0666b4dce503d101f15697e4a49"},"schema_version":"1.0","source":{"id":"1410.8328","kind":"arxiv","version":1}},"canonical_sha256":"495bb6b1ee07108170716162e23629bd7c93ac8684523411347d915c9a261f56","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"495bb6b1ee07108170716162e23629bd7c93ac8684523411347d915c9a261f56","first_computed_at":"2026-05-18T02:39:00.134097Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:39:00.134097Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M6rKsCLoCC54Zj1EkHqGhckAyWJhcSK5AEoEcoCpAqf74WWZmCYg1hGaOrwX7iK9yzSN1F8zGEeK4WKSm0GyDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:39:00.134601Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.8328","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8333e74af05d9c21f35974e423cea721aa1c1eb3969ab26d31fbb1c28ba295d0","sha256:219c194541dbe789e73f2951e306ce353f3b866557db06b481639343a5dc5d80"],"state_sha256":"35d05b4fb182c7f26da587cf3bf22d3e89402c9cc625f79e7d211f87983a8adc"}