On Generalized Sierpi\'{n}ski Graphs
Juan A. Rodr\'iguez-Vel\'azquez, Erick D. Rodr\'iguez-Bazan, Alejandro, Estrada-Moreno
TL;DR
This paper derives explicit formulas for key graph parameters of generalized Sierpiński graphs based on the properties of their base graphs, enhancing understanding of their structural characteristics.
Contribution
It provides the first closed-form expressions for chromatic, vertex cover, clique, and domination numbers of generalized Sierpiński graphs in terms of the base graph parameters.
Findings
Closed formulas for chromatic numbers
Explicit expressions for vertex cover numbers
Formulas for clique and domination numbers
Abstract
In this paper we obtain closed formulae for several parameters of generalized Sierpi\'{n}ski graphs in terms of parameters of the base graph . In particular, we focus on the chromatic, vertex cover, clique and domination numbers.
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Taxonomy
TopicsAdvanced Graph Theory Research · Graph Labeling and Dimension Problems · Graph theory and applications