1. Hereditarnia 20192019, druge monografije in druga zaključena dela Opis: The booklet contains the abstracts of the talks given at the 22th Hereditarnia Workshop on Graph Properties that was held at the Faculty of Electrical Engineering and Computer Science in Maribor on 21st and 22nd of June, 2019. The workshop attracted 22 participants from 8 countries. All of the participants are researchers in di˙erent areas of graph theory, but at this event they all presented topics connected with (hereditary) graph properties. Themes of the talks encompass a wide range of contemporary graph theory research, notably, various types of graph colorings, graph domination, some graph dimensions matchings and graph products. Beside the abstracts of the plenary speaker (Roman Sotak) and three invited speakers (Tanja Gologranc, Michael A. Henning and Ismael G. Yero), the booklet also contains the abstracts of 7 contributed talks given at the event. Ključne besede: mathematics, graph theory, Hereditarnia, Maribor, Slovenia Objavljeno: 13.12.2019; Ogledov: 385; Prenosov: 132 Celotno besedilo (1,08 MB) Gradivo ima več datotek! Več...

2. LjubljanaLeoben graph theory seminar2017, druge monografije in druga zaključena dela Opis: The booklet contains the abstracts of the talks given at the 30th LjubljanaLeoben Graph Theory Seminar that was held at the Faculty of Natural Sciences and Mathematics in Maribor between 1315 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 (bcoloring, 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, LjubljanaLeoben seminar, Maribor, Slovenia Objavljeno: 08.12.2017; Ogledov: 648; Prenosov: 78 Celotno besedilo (457,62 KB) Gradivo ima več datotek! Več...

3. Omega polynomial revisitedMircea V. Diudea, Sandi Klavžar, 2010, izvirni znanstveni članek Opis: Omega polynomial was proposed by Diudea (Omega Polynomial, Carpath. J. Math., 2006, 22, 4347) to count the opposite topologically parallel edges in graphs, particularly to describe the polyhedral nanostructures. In this paper, the main definitions are reanalyzed and clear relations with other three related polynomials are established. These relations are supported by close formulas and appropriate examples. Ključne besede: mathematics, chemical graph theory, counting polynomials, Ommega polynomial, Theta polynomial, Pi polynomial, PI index, Sadhana polynomial, ClujIlmenau index, CI index Objavljeno: 24.08.2017; Ogledov: 463; Prenosov: 68 Celotno besedilo (263,85 KB) Gradivo ima več datotek! Več...

4. Roman domination number of the Cartesian products of paths and cyclesPolona Repolusk, Janez Žerovnik, 2012, izvirni znanstveni članek Opis: Roman domination is a historically inspired variety of general domination such that every vertex is labeled with labels from $\{0,1,2\}$. Roman domination number is the smallest of the sums of labels fulfilling condition that every vertex, labeled 0, has a neighbor, labeled 2. Using algebraic approach we give ▫$O(C)$▫ time algorithm for computing Roman domination number of special classes of polygraphs (rota and fasciagraphs). By implementing the algorithm we give formulas for Roman domination number of the Cartesian products of paths and cycles ▫$P_n \Box P_k$▫, ▫$P_n \Box C_k$▫ for ▫$k \leq 8$▫ and ▫$n \in {\mathbb N}$▫ and for ▫$C_n \Box P_k$▫ and ▫$C_n \Box C_k$▫ for ▫$k \leq 5$▫, ▫$n \in {\mathbb N}$▫. We also give a list of Roman graphs among investigated families. Ključne besede: graph theory, Roman domination number, Cartesian product, polygraphs, path algebra Objavljeno: 23.08.2017; Ogledov: 646; Prenosov: 153 Celotno besedilo (719,06 KB) Gradivo ima več datotek! Več...

5. Altered Wiener indicesDamir Vukičević, Janez Žerovnik, 2005, izvirni znanstveni članek Opis: Recently Nikolić, Trinajstić and Randić put forward a novel modification ▫$^mW(G)$▫ of the Wiener number ▫$W(G)$▫, called modified Wiener index, which definition was generalized later by Gutman and the present authors. Here we study another class of modified indices defined as ▫$W_{min,λ}(G) = ∑(V(G)^λm_G(u,ν)^λ−m_G(u,ν)^{2λ})$▫ and show that some of the important properties of ▫$W(G)$▫, ▫$^mW(G)$▫ and ▫$^λW(G)$▫ are also properties of ▫$W_{min,λ}(G)$▫, valid for most values of the parameter λ. In particular, if ▫$T_n$▫ is any nvertex tree, different from the nvertex path ▫$P_n$▫ and the nvertex star ▫$S_n$▫, then for any λ ≥ 1 or λ < 0, ▫$^W_{min,λ}(P_n) > W_{min,λ}(T_n)>W_{min,λ}(S_n)$▫. Thus for these values of the parameter λ, ▫$W_{min,λ}(G)$▫ provides a novel class of structuredescriptors, suitable for modeling branchingdependent properties of organic compounds, applicable in QSPR and QSAR studies. We also demonstrate that if trees are ordered with regard to ▫$W_{min,λ}(G)$▫ then, in the general case, this ordering is different for different λ. Ključne besede: mathematics, chemical graph theory, Wiener index, modified Wiener index Objavljeno: 17.08.2017; Ogledov: 525; Prenosov: 77 Celotno besedilo (991,46 KB) Gradivo ima več datotek! Več...

6. The number of moves of the largest disc in shortest paths on Hanoi graphsSimon Aumann, Katharina Götz, Andreas Hinz, Ciril Petr, 2014, izvirni znanstveni članek Opis: In contrast to the widespread interest in the FrameStewart conjecture (FSC) about the optimal number of moves in the classical Tower of Hanoi task with more than three pegs, this is the first study of the question of investigating shortest paths in Hanoi graphs ▫$H_p^n$▫ in a more general setting. Here ▫$p$▫ stands for the number of pegs and ▫$n$▫ for the number of discs in the Tower of Hanoi interpretation of these graphs. The analysis depends crucially on the number of largest disc moves (LDMs). The patterns of these LDMs will be coded as binary strings of length ▫$p1$▫ assigned to each pair of starting and goal states individually. This will be approached both analytically and numerically. The main theoretical achievement is the existence, at least for all ▫$n \geqslant p(p2)$▫, of optimal paths where ▫$p1$▫ LDMs are necessary. Numerical results, obtained by an algorithm based on a modified breadthfirst search making use of symmetries of the graphs, lead to a couple of conjectures about some cases not covered by our ascertained results. These, in turn, may shed some light on the notoriously open FSC. Ključne besede: graph theory, Tower of Hanoi, Hanoi graphs, shortest paths, symmetries, breadthfirst search Objavljeno: 14.08.2017; Ogledov: 803; Prenosov: 157 Celotno besedilo (376,70 KB) Gradivo ima več datotek! Več...

7. Linear recognition of generalized Fibonacci cubes $Q_h (111)$Yoomi Rho, Aleksander Vesel, 2016, izvirni znanstveni članek Opis: The generalized Fibonacci cube $Q_h(f)$ is the graph obtained from the $h$cube $Q_h$ by removing all vertices that contain a given binary string $f$ as a substring. In particular, the vertex set of the 3rd order generalized Fibonacci cube $Q_h(111)$ is the set of all binary strings $b_1b_2 ... b_h$ containing no three consecutive 1’s. We present a new characterization of the 3rd order generalized Fibonacci cubes based on their recursive structure. The characterization is the basis for an algorithm which recognizes these graphs in linear time. Ključne besede: graph theory, Fibonacci cubes, recognition algorithm Objavljeno: 10.07.2017; Ogledov: 580; Prenosov: 90 Celotno besedilo (803,81 KB) Gradivo ima več datotek! Več...

8. Efficient open domination in graph productsDorota Kuziak, Iztok Peterin, Ismael G. Yero, 2014, izvirni znanstveni članek Opis: A graph ▫$G$▫ is an efficient open domination graph if there exists a subset ▫$D$▫ of ▫$V(G)$▫ for which the open neighborhoods centered in vertices of ▫$D$▫ form a partition of ▫$V(G)$▫. We completely describe efficient open domination graphs among lexicographic, strong, and disjunctive products of graphs. For the Cartesian product we give a characterization when one factor is ▫$K_2$▫. Ključne besede: graph theory, efficient open domination, graph products, total domination Objavljeno: 10.07.2017; Ogledov: 569; Prenosov: 77 Celotno besedilo (804,78 KB) Gradivo ima več datotek! Več...

9. Covering codes in Sierpiński graphsLaurent Beaudou, Sylvain Gravier, Sandi Klavžar, Matjaž Kovše, Michel Mollard, 2010, izvirni znanstveni članek Opis: Za dani graf ▫$G$▫ in celi števili ▫$a$▫ in ▫$b$▫ je ▫$(a,b)$▫koda grafa ▫$G$▫ množica vozlišč ▫$C$▫, tako da ima vsako vozlišče iz ▫$C$▫ natanko ▫$a$▫ sosedov v ▫$C$▫, vsako drugo vozlišče pa natanko ▫$b$▫ sosedov v ▫$C$▫. V tem prispevku klasificiramo števila ▫$a$▫ in ▫$b$▫, za katera obstajajo ▫$(a,b)$▫kode v grafih Sierpińskega. Ključne besede: graph theory, codes in graphs, perfect codes, Sierpiński graphs Objavljeno: 10.07.2017; Ogledov: 510; Prenosov: 90 Celotno besedilo (786,68 KB) Gradivo ima več datotek! Več...

10. 