13 citations · 21 across the 20 of their papers we have counts for
25 papers
On the odd independence number of the Queen graph
Martin Knor, Jelena Sedlar, Riste Škrekovski
A set S of vertices of a graph is odd independent if it is independent and every vertex outside S has either zero or an odd number of neighbors in S. The largest size of such a set…
Counterexamples to two conjectures on (1, 2)-domination in cubic graphs
Martin Knor, Jelena Sedlar, Riste Škrekovski
Let G be a cubic graph of order n. The induced cycles vertex number cind(G) is the largest size of a vertex set that induces a 2-regular subgraph of G. By gamma_1,2(G) we denote th…
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 Škrekovski +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 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…
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…