Sharp bounds for the number of maximal independent sets in trees of fixed diameter
Alexander Dainiak
TL;DR
This paper establishes precise bounds on the maximum and minimum number of maximal independent sets in trees with a given number of vertices and fixed diameter, characterizing all extremal trees.
Contribution
It provides exact extremal bounds and characterizes all extremal trees for the number of maximal independent sets in trees with fixed diameter.
Findings
Sharp lower and upper bounds for the number of maximal independent sets
Complete characterization of extremal trees up to isomorphism
Results applicable to trees with fixed number of vertices and diameter
Abstract
We obtain sharp lower and upper bounds for the number of maximal (under inclusion) independent sets in trees with fixed number of vertices and diameter. All extremal trees are described up to isomorphism.
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Taxonomy
TopicsGraph theory and applications · Limits and Structures in Graph Theory · Advanced Graph Theory Research