On unicyclic graphs of metric dimension 2 with vertices of degree 4

• Date: 2019
• Main Authors: Dudenko, Marharyta, Oliynyk, Bogdana
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2019
• Subjects: graph; distance; metric dimension; unicyclic graph; 05C12
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1265
• Journal Title: Algebra and Discrete Mathematics

We show that if \(G\) is a unicyclic graph with metric dimension \(2\) and \(\{a,b\}\) is a metric basis of \(G\) then the degree of any vertex \(v\) of \(G\)  is at most \(4\) and degrees of both \(a\) and \(b\) are at most \(2\). The constructions of unispider and semiunispider graphs  and their k...