20.500.12556/DiRROS-23099 Injective colorings of Sierpiński-like graphs and Kneser graphs Two relationships between the injective chromatic number and, respectively, chromatic number and chromatic index, are proved. They are applied to determine the injective chromatic number of Sierpiński graphs and to give a short proof that Sierpiński graphs are Class 1. Sierpiński-like graphs are also considered, including generalized Sierpiński graphs over cycles and rooted products. It is proved that the injective chromatic number of a rooted product of two graphs lies in a set of six possible values. Sierpiński graphs and Kneser graphs $K(n,r)$ are considered with respect of being perfect injectively colorable, where a graph is perfect injectively colorable if it has an injective coloring in which every color class forms an open packing of largest cardinality. In particular, all Sierpiński graphs and Kneser graphs $K(n,r)$ with $n\ge 3r-1$, are perfect injectively colorable, while $K(7,3)$ is not. injective coloring injective chromatic number perfect injectively colorable graph Sierpiński graphs Kneser graphs rooted product graph injektivno barvanje injektivno kromatično število popolno injektivno obarljiv graf grafi Sierpińskega Kneserjevi grafi korenski produkt grafov true false true Angleški jezik Slovenski jezik Neznano 2025-07-25 09:06:28 2025-07-25 09:06:29 2025-10-24 03:53:09 0000-00-00 00:00:00 2025 0 0 22 str. iss. 4, article no. 83 Vol. 41 Aug. 2025 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2025-08-01 519.17 0911-0119 10.1007/s00373-025-02952-3 243802627 s00373-025-02952-3.pdf s00373-025-02952-3.pdf 1 8406140D4BA7AE756E30E322A1DF27C8 7d39332888b83173a5298b52102a29d7b06eb4f0f81ba44ef553eb2e9ccc6611 71c62d36-6926-11f0-9bb7-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=33858 https://link.springer.com/article/10.1007/s00373-025-02952-3 1 e565965d-6925-11f0-9bb7-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=33857 Inštitut za matematiko, fiziko in mehaniko 0 0 0