25 citations · 35 across the 6 of their papers we have counts for
9 papers
On the Wiener-like root-indices of graphs
Simon Brezovnik, Matthias Dehmer, Niko Tratnik +1
In this paper, we examine roots of graph polynomials where those roots can be considered as structural graph measures. More precisely, we prove analytical results for the roots of…
Resonance graphs that are daisy cubes: from hypercubes to independent sets via resonant sets
Simon Brezovnik, Zhongyuan Che, Niko Tratnik +1
Let be a plane elementary bipartite graph whose infinite face is forcing. We provide a bijection between the set of maximal hypercubes of its resonance graph and the set of max…
Resonance graphs of plane bipartite graphs as daisy cubes
Simon Brezovnik, Zhongyuan Che, Niko Tratnik +1
We characterize plane bipartite graphs whose resonance graphs are daisy cubes, and therefore generalize related results on resonance graphs of benzenoid graphs, catacondensed even…
Outerplane bipartite graphs with isomorphic resonance graphs
Simon Brezovnik, Zhongyuan Che, Niko Tratnik +1
We present novel results related to isomorphic resonance graphs of 2-connected outerplane bipartite graphs. As the main result, we provide a structure characterization for 2-connec…
General cut method for computing Szeged-like topological indices with applications to molecular graphs
Simon Brezovnik, Niko Tratnik
Szeged, PI and Mostar indices are some of the most investigated distance-based molecular descriptors. Recently, many different variations of these topological indices appeared in t…
Grundy domination and zero forcing in regular graphs
Boštjan Brešar, Simon Brezovnik
Given a finite graph , the maximum length of a sequence of vertices in such that each dominates a vertex that is not dominated by any vertex in $\{v…
Resonance graphs of catacondensed even ring systems
Simon Brezovnik, Niko Tratnik, Petra Žigert Pleteršek
A catacondensed even ring system (shortly CERS) is a simple bipartite 2-connected outerplanar graph with all vertices of degree 2 or 3. In this paper, we investigate the resonance…
Resonantly Equivalent Catacondensed Even Ring Systems
Simon Brezovnik, Niko Tratnik, Petra Žigert Pleteršek
In this paper we generalize the binary coding procedure of perfect matchings from catacondensed benzenoid graphs to catacondensed even ring systems (also called cers). Next, we stu…
New methods for calculating the degree distance and the Gutman index
Simon Brezovnik, Niko Tratnik
In the paper we develop new methods for calculating the two well-known topological indices, the degree-distance and the Gutman index. Firstly, we prove that the Wiener index of a d…