36 citations · 181 across the 21 of their papers we have counts for
29 papers
Isomorphic daisy cubes based on their -graphs
Zhongyuan Che, Niko Tratnik, Petra Žigert Pleteršek
We prove that if and are daisy cubes whose -graphs are forests, then and are isomorphic if and only if their -graphs are isomorphic. The result is applied to…
Efficient graph similarity assessment method based on vectors of topological indices
Matthias Dehmer, Izudin Redžepović, Niko Tratnik +1
Measuring similarity between complex objects is a fundamental task in many scientific fields. When objects are represented as graphs, graph similarity/distance measures offer a pow…
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…
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…
Computing weighted Szeged and PI indices from quotient graphs
Niko Tratnik
The weighted Szeged index and the weighted vertex-PI index of a connected graph are defined as and $wPI_v(G) = \…
Computing the Mostar index in networks with applications to molecular graphs
Niko Tratnik
Recently, a bond-additive topological descriptor, named as the Mostar index, has been introduced as a measure of peripherality in networks. For a connected graph , the Mostar in…
Generalized cut method for computing the edge-Wiener index
Niko Tratnik
The edge-Wiener index of a connected graph is defined as the Wiener index of the line graph of . In this paper it is shown that the edge-Wiener index of an edge-weighted gra…
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…
Formula for calculating the Wiener polarity index with applications to benzenoid graphs and phenylenes
Niko Tratnik
The Wiener polarity index of a graph is defined as the number of unordered pairs of vertices at distance three. In recent years, this topological index was extensively studied sinc…
The edge-Hosoya polynomial of benzenoid chains
Niko Tratnik, Petra Žigert Pleteršek
The Hosoya polynomial is a well known vertex-distance based polynomial, closely correlated to the Wiener index and the hyper-Wiener index, which are widely used molecular-structure…
The Wiener polarity index of benzenoid systems and nanotubes
Niko Tratnik
In this paper, we consider a molecular descriptor called the Wiener polarity index, which is defined as the number of unordered pairs of vertices at distance three in a graph. Mole…
Resonance Graphs and Perfect Matchings of Graphs on Surfaces
Niko Tratnik, Dong Ye
Let be a graph embedded in a surface and let be a set of even faces of (faces bounded by a cycle of even length). The resonance graph of with respect to $\…
On the Steiner hyper-Wiener index of a graph
Niko Tratnik
In this paper, we study the Steiner hyper-Wiener index of a graph, which is obtained from the standard hyper-Wiener index by replacing the classical graph distance with the Steiner…
On the Clar Number of Benzenoid Graphs
Nino Bašić, István Estélyi, Riste Škrekovski +1
A Clar set of a benzenoid graph is a maximum set of independent alternating hexagons over all perfect matchings of . The Clar number of , denoted by , is the…
Predicting Melting Points by the Graovac-Pisanski Index
Matevž Črepnjak, Niko Tratnik, Petra Žigert Pleteršek
Theoretical molecular descriptors alias topological indices are a convenient means for expressing in a numerical form the chemical structure encoded in a molecular graph. The struc…
The Graovac-Pisanski index of connected bipartite graphs with applications to hydrocarbon molecules
Matevž Črepnjak, Martin Knor, Niko Tratnik +1
The Graovac-Pisanski index, also called the modified Wiener index, was introduced in 1991 and represents an extension of the original Wiener index, because it considers beside the…
The Edge-Wiener Index, the Szeged Indices and the PI Index of Benzenoid Systems in Sub-Linear Time
Matevž Črepnjak, Niko Tratnik
In this paper, we investigate the edge-Wiener index, the Szeged index, the edge-Szeged index, and the PI index, which are some of the most studied distance-based topological indice…
The Graovac-Pisanski Index of Armchair Nanotubes
Niko Tratnik, Petra Žigert Pleteršek
The Graovac-Pisanski index, which is also called the modified Wiener index, considers the symmetries and the distances in molecular graphs. Carbon nanotubes are molecules made of c…
The Graovac-Pisanski Index of Zig-Zag Tubulenes and the Generalized Cut Method
Niko Tratnik
The Graovac-Pisanski index, which is also called the modified Wiener index, was introduced in 1991 by A. Graovac and T. Pisanski. This variation of the classical Wiener index takes…