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364. A method for computing the edge-Hosoya polynomial with application to phenylenesMartin Knor, Niko Tratnik, 2023, izvirni znanstveni članek Povzetek: The edge-Hosoya polynomial of a graph is the edge version of the famous Hosoya polynomial. Therefore, the edge-Hosoya polynomial counts the number of (unordered) pairs of edges at distance $k \ge 0$ in a given graph. It is well known that this polynomial is closely related to the edge-Wiener index and the edge-hyper-Wiener index. As the main result of this paper, we greatly generalize an earlier result by providing a method for calculating the edge-Hosoya polynomial of a graph $G$ which is obtained by identifying two edges of connected bipartite graphs $G_1$ and $G_2$. To show how the main theorem can be used, we apply it to phenylene chains. In particular, we present the recurrence relations and a linear time algorithm for calculating the edge-Hosoya polynomial of any phenylene chain. As a consequence, closed formula for the edge-Hosoya polynomial of linear phenylene chains is derived.
Ključne besede: edge-Hosoya polynomial, graphs, phenylenes
Objavljeno v DiRROS: 18.03.2024; Ogledov: 88; Prenosov: 31
 Celotno besedilo (530,53 KB) |
365. How to compute the M-polynomial of (chemical) graphsEmeric Deutsch, Sandi Klavžar, Gašper Domen Romih, 2023, izvirni znanstveni članek Povzetek: Let $G$ be a graph and let $m_{i,j}(G)$, $i,j\ge 1$, be the number of edges $uv$ of ▫$G$▫ such that $\{d_v(G), d_u(G)\} = \{i,j\}$. The M-polynomial of $G$ is $M(G;x,y) = \sum_{i\le j} m_{i,j}(G)x^iy^j$. A general method for calculating the M-polynomials for arbitrary graph families is presented. The method is further developed for the case where the vertices of a graph have degrees 2 and $p$, where $p\ge 3$, and further for such planar graphs. The method is illustrated on families of chemical graphs.
Ključne besede: M-polynomial, chemical graph, planar graph
Objavljeno v DiRROS: 18.03.2024; Ogledov: 84; Prenosov: 33
Celotno besedilo (376,13 KB) |
366. Qualitative analysis of the minimal Higgins model of glycolysisBrigita Ferčec, Matej Mencinger, Tatjana Petek, Orhan Ozgur Aybar, Ilknur Kusbeyzi Aybar, 2023, izvirni znanstveni članek Povzetek: Glycolysis, one of the leading metabolic pathways, involves many
different periodic oscillations emerging at positive steady states of
the biochemical models describing this essential process. One of
the models employing the molecular diffusion of intermediates is
the Higgins biochemical model to explain sustained oscillations. In
this paper, we investigate the center-focus problem for the minimal
Higgins model for general values of the model parameters with the
help of computational algebra. We demonstrate that the model
always has a stable focus point by finding a general form of the first
Lyapunov number. Then, varying two of the model parameters, we
obtain the first three coefficients of the period function for the stable focus point of the model and prove that the singular point is actually a bi-weak monodromic equilibrium point of type $[1, 2]$. Additionally, we prove that there are two (small) intervals for a chosen parameter $a > 0$ for which one critical period bifurcates from this singular point after small perturbations.
Ključne besede: biological processes, biochemical models, glycolysis
Objavljeno v DiRROS: 18.03.2024; Ogledov: 91; Prenosov: 45
Celotno besedilo (837,28 KB)
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368. CT colonography in detection of colorectal carcinomaAmela Sofić, Šerif Beslić, Igor Kocijančič, Nedžad Šehović, 2010, izvirni znanstveni članek Povzetek: Background. Diagnostic methods used in screening and detectingand 2 lipomas,and 2 lipomas, among tumours there were 55 adenocarcinomas and 1 lymphoma. Results showed CT colonography among tumours there were 55 adenocarcinomas and 1 lymphoma. Results showed CTsensitivity to polyps to be 89.7%, barium enema 48.7%, and colonoscopy 94.9%. Sensitivity to tumours of CT colonography colonography colorectal CT barium enema followed by colonoscopy wereand colonoscopy was 100% and of barium enema 94.6%. Specificities and PPV were 100% in all procedures. The performed. After thesensitivity to polyps to be 89.7%, barium enema 48.7%, andcomfort assessment showed CT colonography as the far most comfortable out of three procedures. colonoscopy 94.9%. Sensitivity to tumours of CT colonography procedures a comfort assessment was done in all colonography. The aim of thisand colonoscopy was 100% and of barium enema 94.6%. Specificities and PPV were 100% in all procedures. The study was to establish diagnostic accuracy andpatients. Diagnostic positive comfort assessment showed CT colonography as the far most comfortable out of three procedures. results were verified by the pato-histological examination. Sensitivity, specificity, positive comfort of CT colonography compared carcinoma are digitorectal examination,topredicative value (PPV) and negative predicative value (NPV) were calculated for each procedure.
Ključne besede: CT colonography, barium enema, colonoscopy, colorectal polyp, colorectal carcinoma
Objavljeno v DiRROS: 18.03.2024; Ogledov: 90; Prenosov: 30
Celotno besedilo (933,29 KB) |
369. Resonance graphs and a binary coding of perfect matchings of outerplane bipartite graphsSimon Brezovnik, Niko Tratnik, Petra Žigert Pleteršek, 2023, izvirni znanstveni članek Povzetek: 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 DiRROS: 18.03.2024; Ogledov: 80; Prenosov: 32
Celotno besedilo (433,15 KB) |
370. Zhang-Zhang polynomials of phenylenes and benzenoid graphsNiko Tratnik, 2024, izvirni znanstveni članek Povzetek: The aim of this paper is to study some variations of the Zhang-Zhang polynomial for phenylenes, which can be obtained as special cases of the multivariable Zhang-Zhang polynomial. Firstly, we prove the equality between the first Zhang-Zhang polynomial of a phenylene and the generalized Zhang-Zhang polynomial of some benzenoid graph, which enables us to prove also the equality between the first Zhang-Zhang polynomial and the generalized cube polynomial of the resonance graph. Next, some results on the roots of the second Zhang-Zhang polynomial of phenylenes are provided and another expression for this polynomial is established. Finally, we give structural interpretation for (partial) derivatives of different Zhang-Zhang polynomials.
Ključne besede: graph theory, resonance graphs, polynomials
Objavljeno v DiRROS: 18.03.2024; Ogledov: 88; Prenosov: 35
Celotno besedilo (487,12 KB) |
