LAUSR

For a nondecreasing sequence of integers $$S=(s_1, s_2, \ldots )$$ S = ( s 1 , s 2 , … ) an S -packing k -coloring of a graph G is a mapping from V ( G ) to $$\{1, 2,\ldots ,k\}$$ { 1 , 2 , … , k } such that vertices with color i have pairwise distance greater than $$s_i$$ s i . By setting $$s_i = d + \lfloor \frac{i-1}{n} \rfloor $$ s i = d + ⌊ i - 1 n ⌋ we obtain a ( d ,  n )-packing coloring of a graph G . The smallest integer k for which there exists a ( d ,  n )-packing coloring of G is called the ( d ,  n )-packing chromatic number of G . In the special case when d and n are both equal to one we obtain the packing chromatic number of G . We determine the packing chromatic number of base-3 Sierpiński graphs and provide new results on ( d ,  n )-packing chromatic colorings for this class of graphs. By using a dynamic algorithm, we establish the packing chromatic number for H -graphs.