Packing coloring of generalized Sierpinski graphs
Danilo Korze, Aleksander Vesel

TL;DR
This paper investigates the packing chromatic number of various Sierpinski-type graphs, establishing exact values for some families and bounds for others, advancing understanding of graph coloring in fractal-like structures.
Contribution
It determines the packing chromatic numbers for generalized Sierpinski graphs based on paths, cycles, and small graphs, and provides an upper bound for Sierpinski-triangle graphs.
Findings
Exact packing chromatic numbers for $S^n_G$ with $G$ as a path or cycle (except cycle of length five).
Bounded the packing chromatic number of $ST_4^n$ by 20.
Extended understanding of coloring properties in fractal and recursive graph families.
Abstract
The packing chromatic number of a graph is the smallest integer such that the vertex set can be partitioned into sets , with the condition that vertices in have pairwise distance greater than . 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 where 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 is bounded from above by 20.
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Taxonomy
TopicsLimits and Structures in Graph Theory · Graph Labeling and Dimension Problems · Advanced Graph Theory Research
