7 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…
Counting geodesic paths in graphs
Martin Knor, Jelena Sedlar, Riste Å krekovski +1
A geodesic is a shortest path which connects a pair of vertices of a graph G. In this paper we define the geodesic subpath number gpn(G) of a graph G as the number of geodesics in…
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…
Some results on -irregularity
Slobodan Filipovski, Darko Dimitrov, Martin Knor +1
The -irregularity (or sigma total index) is a graph invariant which is defined as where denotes the degree o…
Extremizing antiregular graphs by modifying total -irregularity
Martin Knor, Riste Å krekovski, Slobodan Filipovski +1
The total -irregularity is given by where indicates the degree of a vertex within the g…