Graphs with minimal well-covered dimension
Gabriella Clemente

TL;DR
This paper investigates the well-covered dimension of certain graph classes, showing that some graphs, including chordal and Sierpinski gasket graphs, have well-covered dimension equal to their simplicial clique number, generalizing previous results.
Contribution
It introduces a class of graphs with well-covered dimension equal to the simplicial clique number, extending known results to new graph families including Sierpinski gasket graphs.
Findings
Graphs with well-covered dimension equal to the simplicial clique number include chordal and certain other graphs.
All Sierpinski gasket graphs of order at least 2 have well-covered dimension 3.
The class of graphs studied generalizes previous results on chordal graphs.
Abstract
There is a class of graphs with well-covered dimension equal to the simplicial clique number that contains all chordal graphs and infinitely many other graphs. These graphs generalize a result by Brown and Nowakowski on the well-covered dimension of chordal graphs. Furthermore, each member of the infinite family of Sierpinski gasket graphs of order at least has well-covered dimension the simplicial clique number.
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Taxonomy
TopicsGraph Labeling and Dimension Problems · Advanced Graph Theory Research · Limits and Structures in Graph Theory
