4 papers
A complete characterization of maximally σ-irregular trees with prescribed maximum degree
Martin Knor, Jelena Sedlar, Riste Škrekovski
The sigma-irregularity of a graph G = (V, E) is defined as the sum, over all edges uv in E, of (d(u) - d(v))^2, where d(u) denotes the degree of vertex u. A tree on n vertices with…
The subpath number of cactus graphs
Martin Knor, Jelena Sedlar, Riste Å krekovski +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…
Invitation to the subpath number
Martin Knor, Jelena Sedlar, Riste Å krekovski +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…
Fault tolerance of metric basis can be expensive
Martin Knor, Jelena Sedlar, Riste Å krekovski
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…