Diameters of commuting graphs of matrices over semirings
David Dol\v{z}an, Damjana Kokol Bukov\v{s}ek, Polona Oblak
TL;DR
This paper determines the diameters of commuting graphs for matrices over various semirings, including Boolean, tropical, and general commutative semirings, providing new bounds and exact values.
Contribution
It computes the diameters of commuting graphs over specific semirings and establishes lower bounds for general cases, advancing understanding of matrix commutativity in algebraic structures.
Findings
Diameters calculated for matrices over Boolean and tropical semirings.
Lower bounds established for commuting graphs over certain semirings.
Exact diameters obtained for specific classes of semirings.
Abstract
We calculate the diameters of commuting graphs of matrices over the binary Boolean semiring, the tropical semiring and an arbitrary nonentire commutative semiring. We also find the lower bound for the diameter of the commuting graph of the semiring of matrices over an arbitrary commutative entire antinegative semiring.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsCommutative Algebra and Its Applications · Rings, Modules, and Algebras · Algebraic structures and combinatorial models