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This research aims to develop an algorithmic framework for counting independent sets in irregular graphene-like graphs with asymmetries.

June 10, 2026SymmetryOpen Access

Counting Independent Sets in Graphene-like Graphs with Asymmetries Through Hamiltonian Traversals and Minimal Induced Pathwidth

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This research aims to develop an algorithmic framework for counting independent sets in irregular graphene-like graphs with asymmetries.
Proposed an asymmetry-aware algorithm based on Hamiltonian traversals.
Defined a traversal-induced pathwidth parameter w(G) to manage non-local dependencies.
Utilized a dynamic programming scheme over a reduced state space for computation.
The algorithm runs in time O2w(G)·poly(n), demonstrating fixed-parameter tractability with respect to w(G).
Asymmetry-aware traversal strategies improved exact enumeration of molecular descriptors in irregular mesh graph families.
Provided a robust computational framework for analyzing structures with topological defects like Stone–Wales transformations.

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Randomized trial shows efficient enumeration of independent sets in graphene-like graphs, suggesting a new computational framework.

Romero et al. (2026) studied this question.

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