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In [Total dominator chromatic number of a graph, submitted] the author initialed to study this number in graphs and obtained some important results. Here, we continue it in Mycieleskian graphs. We show that the total dominator chromatic number of the Mycieleskian of a graph $G$ belongs to between $\\chi_d^t(G)+1$"},"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":"1307.7706","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-07-29T07:29:27Z","cross_cats_sorted":[],"title_canon_sha256":"922bcfdb6703862c37d7284bcc64e397cf3a838c40f3b02badddcbc37ba327ea","abstract_canon_sha256":"d2a187e57d89a28a20eb1ff9b5ab0f41f2d046b72c51d637a4377eba9cce0ee4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:43.651904Z","signature_b64":"nejs7qiNwKb1xswU8vpLGbK+wDpkEoEi7bisU04nk+YlULQ8I8TAjHSaL6az3W+xsuU1eroqIUxBAQ4o/JG4Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e1ce40f1ef74c1595de0c8b29083eddbc06632c687e2f30c3c84676723478a1","last_reissued_at":"2026-05-17T23:43:43.651408Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:43.651408Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Total dominator chromatic number and Mycieleskian graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Adel P. 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