3 papers
math.CO2025
The subpath number of cactus graphs
Martin Knor, Jelena Sedlar, Riste Škrekovski +1
The subpath number of a graph G is defined as the total number of subpaths in G, and it is closely related to the number of subtrees, a well-studied topic in graph theory. This pap…
math.CO2025
Invitation to the subpath number
Martin Knor, Jelena Sedlar, Riste Škrekovski +1
In this paper we count all the subpaths of a given graph G; including the subpaths of length zero, and we call this quantity the subpath number of G. The subpath number is related…
math.CO2024
Fault tolerance of metric basis can be expensive
Martin Knor, Jelena Sedlar, Riste Škrekovski
A set of vertices S is a resolving set of a graph G; if for every pair of vertices x and y in G, there exists a vertex s in S such that x and y differ in distance to s. A smallest…