Discrete Applied Mathematics· 2026Q2
Multiset metric dimension of binomial random graphs
- 0citations
- Q2SCImago
- 2026year
Short summary
We establish bounds for the multiset metric dimension of binomial random graphs G(n, p) with edge probability p such that (n-1)p = \Theta(n^x) for a fixed x in (0,1).
AI-generated from the title and abstract; the full text is not read.
Key points
- Introduces bounds for the multiset metric dimension of binomial random graphs G(n, p).
- Focuses on the regime where (n-1)p = \Theta(n^x) for a fixed x in (0,1).
- Bounds are established to hold with high probability.
- The multiset metric dimension is defined as the minimum size of a vertex subset R, where R uniquely distinguishes vertex pairs by their distance multisets to R.
AI-generated from the title and abstract; the full text is not read.
Abstract
For a graph G = ( V , E ) and a subset R ⊆ V , we say that R is multiset resolving for G if for every pair of vertices v , w , the multisets [ d ( v , r ) : r ∈ R ] and [ d ( w , r ) : r ∈ R ] are distinct, where d ( x , y ) is the graph distance between vertices x and y . The multiset metric dimension of G is the size of a smallest set R ⊆ V that is multiset resolving (or ∞ if no such set exists). This graph parameter was introduced by Simanjuntak, Siagian, and Vitrík in 2017 Rinovia Simanjuntak et al. (2017), and has since been studied for a variety of graph families. We prove bounds which hold with high probability for the multiset metric dimension of the binomial random graph G ( n , p ) in the regime d = ( n − 1 ) p = Θ ( n x ) for fixed x ∈ ( 0,1 ) .
The authors' abstract, as published at the source. Discrete Applied Mathematics, 2026 · DOI ↗
Continue with a free account
Ask the paper: 3 free questions a day about this paper; save it, get its citation, new summaries every day for your field. Takeaways are Premium.
Continue free on the webSign in with Google or Apple; no card needed. You come back to this paper.
On your phone:
Field: Computational Theory and Mathematics
Computational Theory and MathematicsComputer Science