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1.
Microsoft Azure avtentikacija : generiranje in uporaba dostopnih žetonov
Tilen Cokan, 2020, undergraduate thesis

Abstract: Aplikacije pri svojem delovanju koristijo zunanje vire, da jih lahko porabijo potrebujejo dostopne žetone, s katerimi se odobri dostop do varovanih virov. Za pridobitev dostopnega žetona je potrebna avtentikacija in avtorizacija uporabnika, pri tem so nam na voljo različni pristopi s pomočjo avtentikacijske knjižnice Microsoft. Avtorizacija in avtentikacija se izvajata v sklopu standardov OAuth2 in OpenID Connect, vse skupaj pa je del Azure Active Directory. Ena takih aplikacij je interna aplikacija podjetja HRC d.o.o., v kateri je omogočeno samodejno generiranje dostopnega žetona za zunanje storitve Microsoft Graph, ki opravlja branje elektronske pošte. V delu smo podrobneje opisali avtentikacijske pristope standarda OAuth2 in tehnike, uporabljene v rešitvi za interno aplikacijo.
Keywords: dostopni žetoni, avtentikacijske tehnike, Microsoft Graph, JSON žetoni
Published in DKUM: 03.11.2020; Views: 232; Downloads: 31
.pdf Full text (554,43 KB)

2.
Distance-based Invariants and Measures in Graphs
Aleksander Kelenc, 2019, doctoral dissertation

Abstract: This doctoral dissertation is concerned with aspects on distance related topics in graphs. We study three main topics, namely a recently introduced measure called the Hausdorff distance of graphs and two new graph invariants - the edge metric dimension and the mixed metric dimension of graphs. All three topics are part of the metric graph theory since they are tightly connected with the basic concept of distance between two vertices of a graph. The Hausdorff distance is a relatively new measure of the similarity of graphs. The notion of the Hausdorff distance considers a special kind of common subgraph of the compared graphs and depends on the structural properties outside of the common subgraph. We study the Hausdorff distance between certain families of graphs that often appear in chemical graph theory. Next to a few results for general graphs, we determine formulae for the distance between paths and cycles. Previously, there was no known efficient algorithm for the problem of determining the Hausdorff distance between two trees, and in this dissertation we present a polynomial-time algorithm for it. The algorithm is recursive and it utilizes the divide and conquer technique. As a subtask it also uses a procedure that is based on the well-known graph algorithm for finding a maximum bipartite matching. The edge metric dimension is a graph invariant that deals with distinguishing the edges of a graph. Let $G=(V(G),E(G))$ be a connected graph, let $w \in V(G)$ be a vertex, and let $e=uv \in E(G)$ be an edge. The distance between the vertex $w$ and the edge $e$ is given by $d_G(e,w)=\min\{d_G(u,w),d_G(v,w)\}$. A vertex $w \in V(G)$ distinguishes two edges $e_1,e_2 \in E(G)$ if $d_G(w,e_1) \ne d_G(w,e_2)$. A set $S$ of vertices in a connected graph $G$ is an edge metric generator of $G$ if every two distinct edges of $G$ are distinguished by some vertex of $S$. The smallest cardinality of an edge metric generator of $G$ is called the edge metric dimension and is denoted by $dim_e(G)$. The concept of the edge metric dimension is new. We study its mathematical properties. We make a comparison between the edge metric dimension and the standard metric dimension of graphs while presenting some realization results concerning the two. We prove that computing the edge metric dimension of connected graphs is NP-hard and give some approximation results. Moreover, we present bounds and closed formulae for the edge metric dimension of several classes of graphs. The mixed metric dimension is a graph invariant similar to the edge metric dimension that deals with distinguishing the elements (vertices and edges) of a graph. A vertex $w \in V(G)$ distinguishes two elements of a graph $x,y \in E(G)\cup V(G)$ if $d_G(w,x) \ne d_G(w,y)$. A set $S$ of vertices in a connected graph $G$ is a mixed metric generator of $G$ if every two elements $x,y \in E(G) \cup V(G)$ of $G$, where $x \neq y$, are distinguished by some vertex of $S$. The smallest cardinality of a mixed metric generator of $G$ is called the mixed metric dimension and is denoted by $dim_m(G)$. In this dissertation, we consider the structure of mixed metric generators and characterize graphs for which the mixed metric dimension equals the trivial lower and upper bounds. We also give results on the mixed metric dimension of certain families of graphs and present an upper bound with respect to the girth of a graph. Finally, we prove that the problem of determining the mixed metric dimension of a graph is NP-hard in the general case.
Keywords: Hausdorff distance, distance between graphs, graph algorithms, trees, graph similarity, edge metric dimension, edge metric generator, mixed metric dimension, metric dimension
Published in DKUM: 03.08.2020; Views: 642; Downloads: 78
.pdf Full text (800,48 KB)

3.
Hereditarnia 2019 : Book of Abstracts, Maribor, 21st & 22nd June, 2019
2019, other monographs and other completed works

Abstract: 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.
Keywords: mathematics, graph theory, Hereditarnia, Maribor, Slovenia
Published in DKUM: 13.12.2019; Views: 543; Downloads: 173
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4.
Izdelava programske rešitve za izvajanje bibliometričnih raziskav in gradnjo tezavrov iz velikih količin bibliometričnih podatkov : diplomsko delo
Boris Vezenšek, 2019, undergraduate thesis

Abstract: V diplomskem delu je obravnavana bibliometrija in bibliometrične analize, izvedene s pomočjo izdelane programske rešitve. Opisane so tehnologije, uporabljene za rešitev našega problema. Tukaj gre predvsem za delovanje Hadoopovega porazdeljenega datotečnega sistema HDFS in modela MapReduce ter sistema Apache Spark. Opisani sta tudi rešitvi Analysis Services Tabular in Power BI. Na koncu so na izbranih primerih predstavljeni rezultati različnih bibliometričnih analiz v orodju Power BI, ki se napaja iz podatkovnega modela, implementiranega v tem diplomskem delu. Rezultati so prikazani v različni obliki – z vizualizacijami, primernimi za takšno vrsto podatkov.
Keywords: bibliometrija, Hadoop, HDFS, Microsoft Academic Graph, podatki CORE, porazdeljena obdelava, Spark, velepodatki
Published in DKUM: 22.11.2019; Views: 463; Downloads: 42
.pdf Full text (1,93 MB)

5.
Ljubljana-Leoben graph theory seminar : Maribor, 13.-15. September, 2017. Book of abstracts
2017, other monographs and other completed works

Abstract: 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.
Keywords: mathematics, discrete mathematics, graph theory, Ljubljana-Leoben seminar, Maribor, Slovenia
Published in DKUM: 08.12.2017; Views: 815; Downloads: 120
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6.
Wiener index of strong product of graphs
Iztok Peterin, Petra Žigert Pleteršek, 2018, original scientific article

Abstract: The Wiener index of a connected graph ▫$G$▫ is the sum of distances between all pairs of vertices of ▫$G$▫. The strong product is one of the four most investigated graph products. In this paper the general formula for the Wiener index of the strong product of connected graphs is given. The formula can be simplified if both factors are graphs with the constant eccentricity. Consequently, closed formulas for the Wiener index of the strong product of a connected graph ▫$G$▫ with a cycle are derived.
Keywords: Wiener index, graph product, strong product
Published in DKUM: 30.11.2017; Views: 965; Downloads: 343
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7.
Omega polynomial revisited
Mircea V. Diudea, Sandi Klavžar, 2010, original scientific article

Abstract: Omega polynomial was proposed by Diudea (Omega Polynomial, Carpath. J. Math., 2006, 22, 43-47) to count the opposite topologically parallel edges in graphs, particularly to describe the polyhedral nanostructures. In this paper, the main definitions are re-analyzed and clear relations with other three related polynomials are established. These relations are supported by close formulas and appropriate examples.
Keywords: mathematics, chemical graph theory, counting polynomials, Ommega polynomial, Theta polynomial, Pi polynomial, PI index, Sadhana polynomial, Cluj-Ilmenau index, CI index
Published in DKUM: 24.08.2017; Views: 561; Downloads: 76
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8.
Roman domination number of the Cartesian products of paths and cycles
Polona Repolusk, Janez Žerovnik, 2012, original scientific article

Abstract: 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.
Keywords: graph theory, Roman domination number, Cartesian product, polygraphs, path algebra
Published in DKUM: 23.08.2017; Views: 780; Downloads: 174
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9.
Altered Wiener indices
Damir Vukičević, Janez Žerovnik, 2005, original scientific article

Abstract: 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 n-vertex tree, different from the n-vertex path ▫$P_n$▫ and the n-vertex 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 structure-descriptors, suitable for modeling branching-dependent 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.
Keywords: mathematics, chemical graph theory, Wiener index, modified Wiener index
Published in DKUM: 17.08.2017; Views: 638; Downloads: 86
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10.
The number of moves of the largest disc in shortest paths on Hanoi graphs
Simon Aumann, Katharina Götz, Andreas Hinz, Ciril Petr, 2014, original scientific article

Abstract: In contrast to the widespread interest in the Frame-Stewart 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 ▫$p-1$▫ 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 ▫$n \geqslant p(p-2)$▫, of optimal paths where ▫$p-1$▫ LDMs are necessary. Numerical results, obtained by an algorithm based on a modified breadth-first 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.
Keywords: graph theory, Tower of Hanoi, Hanoi graphs, shortest paths, symmetries, breadth-first search
Published in DKUM: 14.08.2017; Views: 933; Downloads: 178
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