Iskanje po katalogu digitalne knjižnice

Opis: In this paper, we firstly focus on catacondensed even ring systems (shortly CERS) without any linearly connected adjacent triple of f inite faces. For such a graph G, we describe a bijection between the set of all perfect matchings (Kekulé structures) of G and the set of all independent sets of the inner dual of G, which enables us to prove the equality between three polynomials: the sextet polynomial of G, the independence polynomial of the inner dual of G, and the newly introduced link polynomial of G. These equalities imply that the number of perfect matchings of G equals the number of resonant sets of G and also the number of independent sets of the inner dual of G. Moreover, we show that the number of edges of the resonance graph of G coincides with the derivative of the mentioned polynomials evaluated at x = 1. Finally, we provide the generalization of the results to all peripherally 2-colorable graphs.
Ključne besede: graph theory, resonance graphs, polynomials
Objavljeno v DKUM: 01.10.2025; Ogledov: 0; Prenosov: 5
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Opis: 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 certain modified graph polynomials and also discuss numerical results. As polynomials, we use, e.g., the Hosoya, the Schultz, and the Gutman polynomial which belong to an interesting family of degree-distance-based graph polynomials; they constitute so-called counting polynomials with non-negative integers as coefficients and the roots of their modified versions have been used to characterize the topology of graphs. Our results can be applied for the quantitative characterization of graphs. Besides analytical results on bounds and convergence, we also investigate other properties of those measures such as their degeneracy which is an undesired aspect of graph measures. It turns out that the measures representing roots of graph polynomials possess high discrimination power on exhaustively generated trees, which outperforms standard versions of these indices. Furthermore, a new measure is introduced that allows us to compare different topological indices in terms of structure sensitivity and abruptness.
Ključne besede: graph theory, Hosoya polynomial, Schultz polynomial, Gutman polynomial, root-index, discrimination power, structure sensitivity
Objavljeno v DKUM: 03.07.2025; Ogledov: 0; Prenosov: 10
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Opis: The aim of this paper is to investigate resonance graphs of $2$-connected outerplane bipartite graphs, which include various families of molecular graphs. Firstly, we present an algorithm for a binary coding of perfect matchings of these graphs. Further, $2$-connected outerplane bipartite graphs with isomorphic resonance graphs are considered. In particular, it is shown that if two $2$-connected outerplane bipartite graphs are evenly homeomorphic, then its resonance graphs are isomorphic. Moreover, we prove that for any $2$-connected outerplane bipartite graph $G$ there exists a catacondensed even ring systems $H$ such that the resonance graphs of $G$ and $H$ are isomorphic. We conclude with the characterization of $2$-connected outerplane bipartite graphs whose resonance graphs are daisy cubes.
Ključne besede: graph theory, resonance graphs, bipartite graphs
Objavljeno v DKUM: 10.12.2024; Ogledov: 0; Prenosov: 12
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Opis: Szeged, Padmakar-Ivan (PI), and Mostar indices are some of the most investigated distance-based Szeged-like topological indices. On the other hand, the polynomials related to these topological indices were also introduced, for example the Szeged polynomial, the edge- Szeged polynomial, the PI polynomial, the Mostar polynomial, etc. In this paper, we introduce a concept of the general Szeged-like polynomial for a connected strength-weighted graph. It turns out that this concept includes all the above mentioned polynomials and also infinitely many other graph polynomials. As the main result of the paper, we prove a cut method which enables us to efficiently calculate a Szeged-like polynomial by using the corresponding polynomials of strength-weighted quotient graphs obtained by a partition of the edge set that is coarser than ▫$\Theta^*$▫-partition. To the best of our knowledge, this represents the first implementation of the famous cut method to graph polynomials. Finally, we show how the deduced cut method can be applied to calculate some Szeged-like polynomials and corresponding topological indices of para-polyphenyl chains and carbon nanocones.
Ključne besede: graph theory, carbon nanocone, topological indices
Objavljeno v DKUM: 25.03.2024; Ogledov: 234; Prenosov: 8
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Opis: The booklet contains the abstracts of the talks given at the 30th Ljubljana-Leoben Graph Theory Seminar that was held at the Faculty of Natural Sciences and Mathematics in Maribor between 13-15 September, 2017. The seminar attracted more than 30 participants from eight countries, all of which are researchers in different areas of graph theory. The topics of the talks encompass a wide range of contemporary graph theory research, notably, various types of graph colorings (b-coloring, packing coloring, edge colorings), graph domination (rainbow domination, Grundy domination, graph security), distinguishing problems, algebraic graph theory, graph algorithms, chemical graph theory, coverings, matchings and also some classical extremal problems. Beside the abstracts of the four invited speakers (Csilla Bujtás, Premysl Holub, Jakub Przybyło, Zsolt Tuza), the booklet contains also the abstracts of 18 contributed talks given at the event.
Ključne besede: mathematics, discrete mathematics, graph theory, Ljubljana-Leoben seminar, Maribor, Slovenia
Objavljeno v DKUM: 08.12.2017; Ogledov: 1625; Prenosov: 227
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