@article{Rajendran2026, 
author = {Gurusamy Rajendran and Sankari Alias Deepa Ramamoorthy and Arockiaraj Sonasalam and Grienggrai Rajchakit},
title = {The Steiner antipodal number of zero-divisor graphs of finite commutative rings},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {2},
pages = {3512-3533},
keywords = {zero-divisor graph, n-eccentricity, n-diameter, Steiner n-antipodal graph, Steiner antipodal number},
url = {https://www.sciopen.com/article/10.3934/math.2026143},
doi = {10.3934/math.2026143},
abstract = {Let    R be a finite commutative ring with unity. The zero-divisor graph    Γ  (  R  ) is defined such that its vertex set comprises all nonzero zero-divisors of    R, with two distinct vertices being adjacent if and only if their product is zero. This study provides a closed-form expression for the    n-eccentricity of each vertex and computes the Steiner antipodal number of    Γ  (  R  ) under the following conditions: (ⅰ)    R  =            Z        m  , (ⅱ)    R is a reduced ring, and (ⅲ)    R is a finite direct product of rings of the form              Z        m  . Moreover, we establish the existence of a zero-divisor graph with a Steiner antipodal number equal to some positive integer    m.}
}