10 papers
Two conjectures on the cospectrality of complete tripartite graphs are false
Irena M. Jovanović, Jelena Sedlar, Riste Škrekovski
For a graph G of order n with adjacency eigenvalues lambda_1(G) >= ... >= lambda_n(G), the cospectrality of G within the set G of all graphs of order n is the smallest spectral dis…
The rich-neighbor chromatic index is linear in the maximum degree
Masaki Kashima, Mirko Petruševski, Jelena Sedlar +1
An edge of a multigraph is rich with respect to a proper edge-coloring if all the edges adjacent to it receive mutually distinct colors, and a proper edge-coloring is a rich-neighb…
Resolutions of two conjectures on the spectral diameter
Irena M. Jovanović, Irena Jovanović, Jelena Sedlar +1
Let be the adjacency spectrum of a graph on vertices. The spectral distance between -vertex graphs and is the Manhattan…
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…
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…
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…
Domination number of modular product graphs
Sergio Bermudo, Iztok Peterin, Jelena Sedlar +1
The modular product of graphs and is a graph on vertex set . Two vertices and of are adjacent…