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math.RA2010★ 11 cited
Diameters of commuting graphs of matrices over semirings
David Dolžan, Damjana Kokol Bukovšek, Polona Oblak
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…
math.RA2010
The zero-divisor graphs of semirings
David Dolžan, Polona Oblak
In this paper we study zero--divisor graphs of rings and semirings. We show that all zero--divisor graphs of (possibly noncommutative) semirings are connected and have diameter les…
math.RA2010
On maximal distances in a commuting graph
Gregor Dolinar, Bojan Kuzma, Polona Oblak
We study maximal distances in the commuting graphs of matrix algebras defined over algebraically closed fields. In particular, we show that the maximal distance can be attained onl…