6 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…
Remarks on proper conflict-free degree-choosability of graphs with prescribed degeneracy
Masaki Kashima, Riste Å krekovski, Rongxing Xu
A proper coloring of is called a proper conflict-free coloring of if for every non-isolated vertex of , there is a color such that $|Ï^{-1}(c)\cap N_G(v)|=…
Results on proper conflict-free list coloring of graphs
Masaki Kashima, Riste Å krekovski, Rongxing Xu
Given a graph and a mapping , an -list assignment of is a function that maps each to a set of at least colors. For an -list…
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…
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…