On the Metric Dimension of Signed Graphs

Shahul Hameed K; Remna K P; Divya T2; Biju K; Rajeevan P; Santhosh G O2; Ramakrishnan K O

On the Metric Dimension of Signed Graphs

Combinatorics 2021-06-24 v1

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

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.

Keywords

signed graphs metric dimension resolving sets negation invariance signed trees

Cite

@article{arxiv.2106.12539,
  title  = {On the Metric Dimension of Signed Graphs},
  author = {Shahul Hameed K and Remna K P and Divya T2 and Biju K and Rajeevan P and Santhosh G O2 and Ramakrishnan K O},
  journal= {arXiv preprint arXiv:2106.12539},
  year   = {2021}
}

On the Metric Dimension of Signed Graphs

Abstract

Keywords

Cite

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