1. A note on the metric and edge metric dimensions of 2-connected graphs
- Author
-
Riste Škrekovski, Martin Knor, and Ismael G. Yero
- Subjects
business.industry ,Applied Mathematics ,0211 other engineering and technologies ,021107 urban & regional planning ,0102 computer and information sciences ,02 engineering and technology ,Edge (geometry) ,01 natural sciences ,Upper and lower bounds ,Graph ,Metric dimension ,Combinatorics ,010201 computation theory & mathematics ,05C12, 05C7 ,Metric (mathematics) ,FOS: Mathematics ,Mathematics - Combinatorics ,Discrete Mathematics and Combinatorics ,Combinatorics (math.CO) ,business ,Subdivision ,Mathematics - Abstract
For a given graph $G$, the metric and edge metric dimensions of $G$, $\dim(G)$ and ${\rm edim}(G)$, are the cardinalities of the smallest possible subsets of vertices in $V(G)$ such that they uniquely identify the vertices and the edges of $G$, respectively, by means of distances. It is already known that metric and edge metric dimensions are not in general comparable. Infinite families of graphs with pendant vertices in which the edge metric dimension is smaller than the metric dimension are already known. In this article, we construct a 2-connected graph $G$ such that $\dim(G)=a$ and ${\rm edim}(G)=b$ for every pair of integers $a,b$, where $4\le b, Comment: 12 pages
- Published
- 2022