@article{Sharma2026, 
author = {Sahil Sharma and Omaima Al Shanqiti and Vijay Kumar Bhat},
title = {Computation of edge metric dimension of zero divisor graph of matrices},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {5},
pages = {12780-12794},
keywords = {metric dimension, ZDG, edge metric dimension, upper triangular matrix, resolving set},
url = {https://www.sciopen.com/article/10.3934/math.2026526},
doi = {10.3934/math.2026526},
abstract = {This paper investigated the resolving parameters of the zero-divisor graph (ZDG) associated with the non-commutative ring of    3  ×  3 upper triangular matrices over the field              Z        2  . The structural complexity of non-commutative matrix rings, especially the difference between left and right zero-divisors, poses special difficulties for graph-theoretic characterization, although the metric dimensions of ZDGs for commutative rings have been well known. For this particular graph structure    G  =  Z  D  G  [      M    3    (            Z        2    )  ], we specifically calculated the metric dimension (       dim    v    (  G  )) and the edge metric dimension (       edim    e    (  G  )). We determined the minimal resolving sets and proved that        dim    v    (  G  )  =  [  11  ] and        edim    e    (  G  )  =  [  13  ] by combining combinatorial proofs with structural decomposition into equivalence classes. A basic framework for calculating the metric dimensions of generalized    n  ×  n matrix rings over finite fields is provided by these findings.}
}