The metric dimension of the total graph of a semiring
David Dol\v{z}an
TL;DR
This paper determines the metric dimension of the total graph derived from the direct product of specific finite commutative semirings, focusing on their zero-divisors and structural properties.
Contribution
It introduces the calculation of the metric dimension for total graphs of a class of semirings, extending graph theory to algebraic structures.
Findings
Calculated the metric dimension for the total graph of certain semirings
Identified conditions under which the zero-divisors set influences the metric dimension
Extended graph-theoretic concepts to algebraic structures like semirings
Abstract
We calculate the metric dimension of the total graph of a direct product of finite commutative antinegative semirings with their sets of zero-divisors closed under addition.
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Taxonomy
TopicsGraph Labeling and Dimension Problems · Fuzzy and Soft Set Theory · Advanced Graph Theory Research