5 citations · 5 across the 3 of their papers we have counts for
5 papers
The metric dimension of the annihilating-ideal graph of a finite commutative ring
David Dolžan
We determine the metric dimension of the annihilating-ideal graph of a local finite commutative principal ring and a finite commutative principal ring with two maximal ideals. We a…
Cholesky decomposition of positive semidefinite matrices over commutative semirings
David Dolžan, Polona Oblak
We prove that over a commutative semiring every symmetric strongly invertible matrix with nonnegative numerical range has a Cholesky decomposition.
Bounds for the completely positive rank of a symmetric matrix over a tropical semiring
David Dolžan, Polona Oblak
In this paper, we find an upper bound for the CP-rank of a matrix over a tropical semiring, according to the vertex clique cover of the graph prescribed by the pattern of the matri…
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…
Invertible and nilpotent matrices over antirings
David Dolžan, Polona Oblak
In this paper we characterize invertible matrices over an arbitrary commutative antiring S and find the structure of GL_n (S). We find the number of nilpotent matrices over an enti…