# On the Metric Dimension of Signed Graphs

Source: [On the Metric Dimension of Signed Graphs](<https://www.sota2.com/research/paper/68fa58331e209131ce9ac111>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T15:11:38.006Z

Authors: Shahul Hameed K, Remna K P, Divya T2, Biju K, Rajeevan P, Santhosh G O2, Ramakrishnan K O

Published: 2021-06-23T17:05:46.000Z

## Abstract

A signed graph $\\Sigma$ is a pair $(G,\\sigma)$, where $G=(V,E)$ is the underlying graph in which each edge is assigned $+1$ or $-1$ by the signature function $\\sigma:E\\rightarrow\\{-1,+1\\}$. In this paper, we extend the extensively applied concepts of metric dimension and resolving sets for unsigned graphs to signed graphs. We analyze the metric dimension of some well known classes of signed graphs including a special case of signed trees. Among other things, we establish that the metric dimension of a signed graph is invariant under negation.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2106.12539>)

[PDF](<https://arxiv.org/pdf/2106.12539.pdf>)