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The minimum number of colors required for all vdecs of $G$ is denoted by $\\chi\\,'_s(G)$ called the vdec chromatic number of $G$. Let $n_d(G)$ denote the number of vertices of degree $d$ in $G$. In this note, we show that a tree $T$ with $n_2(T)\\leq n_1(T)$ holds $\\chi\\,'_s(T)=n_1(T)+1$ if its diameter $D(T)=3$ o"},"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":"1601.02601","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-01-09T02:05:28Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"18e3a401bd2500f2550a2824e754959e5d1633c79ceb7b50fc5523b2acd98052","abstract_canon_sha256":"29024005693df79501dc1baf3359164efa92fd1f9c32cad76a6fd56556cd2159"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:01.965979Z","signature_b64":"aV/8TRnaMlQffVTTrPoE17p8ypZyKZJVodwG5ushSkSv8ZCkVWJQk/n9FaHNPfBfV3cl1whLAYBHJtjzodHpCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5849c1f61665702a5787ef76a5726ea4f29744aa4c560387539d60154f4d02ae","last_reissued_at":"2026-05-18T01:23:01.965328Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:01.965328Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Note On Vertex Distinguishing Edge colorings of Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Bing Yao, Songling Shan","submitted_at":"2016-01-09T02:05:28Z","abstract_excerpt":"A proper edge coloring of a simple graph $G$ is called a vertex distinguishing edge coloring (vdec) if for any two distinct vertices $u$ and $v$ of $G$, the set of the colors assigned to the edges incident to $u$ differs from the set of the colors assigned to the edges incident to $v$. 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