Geodesic
Packing coloring of generalized Sierpinski graphs
Discrete mathematics & theoretical computer science, Tome 21 (2019) no. 3

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The packing chromatic number $\chi_{\rho}(G)$ of a graph $G$ is the smallest integer $c$ such that the vertex set $V(G)$ can be partitioned into sets $X_1, . . . , X_c$, with the condition that vertices in $X_i$ have pairwise distance greater than $i$. In this paper, we consider the packing chromatic number of several families of Sierpinski-type graphs. We establish the packing chromatic numbers of generalized Sierpinski graphs $S^n_G$ where $G$ is a path or a cycle (with exception of a cycle of length five) as well as a connected graph of order four. Furthermore, we prove that the packing chromatic number in the family of Sierpinski-triangle graphs $ST_4^n$ is bounded from above by 20. 
@article{DMTCS_2019_21_3_a6,
     author = {Korze, Danilo and Vesel, Aleksander},
     title = {Packing coloring of generalized {Sierpinski} graphs},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {21},
     number = {3},
     year = {2019},
     doi = {10.23638/DMTCS-21-3-7},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-21-3-7/}
}
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Korze, Danilo; Vesel, Aleksander. Packing coloring of generalized Sierpinski graphs. Discrete mathematics & theoretical computer science, Tome 21 (2019) no. 3. doi: 10.23638/DMTCS-21-3-7

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