11 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…
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…
Remarks on proper conflict-free degree-choosability of graphs with prescribed degeneracy
Masaki Kashima, Riste Škrekovski, 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 …
Results on proper conflict-free list coloring of graphs
Masaki Kashima, Riste Škrekovski, 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 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…
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…