%0 Journal Article 
%A Brešar, Boštjan
%A Klavžar, Sandi
%A Samadi, Babak
%A González Yero, Ismael
%T Injective Colorings of Sierpiński-like Graphs and Kneser Graphs
%D 2025
%@ 1435-5914

%U http://hdl.handle.net/10498/37867
%X 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 ≥ 3r − 1 are perfect injectively colorable, while K(7, 3) is not.
%K Injective coloring
%K Injective chromatic number
%K Perfect injectively colorable graph
%K Sierpiński graph
%K Kneser graph
%K Rooted product graph
%~ Universidad de Cádiz