1. Settling of mesoplastics in an open-channel flowLuka Kevorkijan, Elvis Žic, Luka Lešnik, Ignacijo Biluš, 2022, izvirni znanstveni članek Opis: Pollution of water by plastic contaminants has received increasing attention, owing to
its negative effects on ecosystems. Small plastic particles propagate in water and can travel long
distances from the source of pollution. In order to research the settling motion of particles in
water flow, a small-scale experiment was conducted, whereby spherical plastic particles of varying
diameters were released in an open-channel flow. Three approaches were investigated to numerically
simulate the motion of particles. The numerical simulation results were compared and validated
with experimental data. The presented methods allow for deeper insight into particle motion in
fluid flow and could be extended to a larger scale to predict the propagation of mesoplastics in
natural environments.
Ključne besede: dense discrete phase model, discrete element method, diameter, discrete phase model, mesoplastics, particles, settling
Objavljeno v DKUM: 20.03.2025; Ogledov: 0; Prenosov: 4
 Celotno besedilo (3,51 MB)
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2. Nekateri rezultati o povezanosti in neodvisnih množicah v produktih grafovTjaša Paj Erker, 2018, doktorska disertacija Opis: Doktorska disertacija obravnava nekatere rezultate na grafovskih produktih.
V uvodu bomo na kratko predstavili vsebino doktorske disertacije in ponovili nekatere osnovne pojme teorije grafov, ki jih bomo uporabljali v nadaljevanju.
Prva tema, ki jo bomo predstavili so neodvisne množice v direktnem produktu.
Govorili bomo o velikosti in strukturi največjih neodvisnih množic v direktnem
produktu. Najprej bomo predstavili pomembnejše znane rezultate, nato pa bomo
pokazali, da ima direkten produkt lihe poti in poljubnega grafa, ter direkten produkt sodega cikla in poljubnega grafa največjo neodvisno množico, ki je unija dveh pravokotnikov. Ugotovili bomo, da obstajajo v direktnem produktu sode poti in poljubnega grafa največje neodvisne množice, ki so lahko tudi drugačne oblike ter zapisali natančno karakterizacijo teh največjih neodvisnih množic. Zapisali bomo zadostni pogoji za drevesa, da ima direkten produkt drevesa in poljubnega grafa največjo neodvisno množico
oblike dveh pravokotnikov.
V nadaljevanju bomo raziskali posplošeno 3-povezanost v kartezičnem produktu
grafov. Prikazali bomo več naravnih načinov, kako dobiti 3-presečno
množico S, pri kateri nam graf razpade na vsaj tri komponente. Nato
bomo dokazali, da je eden izmed teh načinov vedno optimalen, če sta G in H
2-povezana grafa na vsaj šestih vozliščih. Tako dobimo natančno vrednost posplošene 3-povezanosti kartezičnega produkta dveh 2-povezanih grafov na vsaj
šestih vozliščih.
Na koncu se bomo ukvarjali z vprašanjem o zgornji meji najmanjšega diametra
krepko orientiranega krepkega produkta. Določili bomo natančno vrednost
najmanjšega diametra krepkega produkta dveh poti.
Ključne besede: direktni produkt, kartezični produkt, krepki produkt, neodvisna
množica, povezanost, posplošena povezanost, diameter, krepka orientacija
Objavljeno v DKUM: 11.12.2018; Ogledov: 1549; Prenosov: 165
Celotno besedilo (603,74 KB) |
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4. The edge fault-diameter of Cartesian graph bundlesIztok Banič, Rija Erveš, Janez Žerovnik, 2009, izvirni znanstveni članek Opis: Kartezični svežnji so posplošitev krovnih grafov in kartezičnih grafovskih produktov. Naj bo ▫$G$▫ nek s povezavami ▫$k_G$▫-povezan graf in ▫${bar{mathcal{D}}_c(G)}$▫ največji premer podgrafov grafa ▫$G$▫ dobljenih z odstranitvijo $▫c < k_G$▫ povezav. Dokazano je, da je ▫${bar{mathcal{D}}_{a+b+1}(G)} le {bar{mathcal{D}}_a(F)} le {bar{mathcal{D}}_b(B)} + 1$▫, če je ▫$G$▫ grafovski sveženj z vlaknom ▫$F$▫ in bazo ▫$B$▫, ▫$a < k_F$▫, ▫$b < k_B▫$. Dokazano je tudi, da je povezanost s povezavami grafovskega svežnja ▫$G▫$ vsaj ▫$k_F + k_B$▫.
Ključne besede: matematika, teorija grafov, kartezični grafovski produkti, kartezični grafovski svežnji, povezavni okvarni premer, mathematics, graph theory, Cartesian graph products, Cartesian graph bundles, edge-fault diameter
Objavljeno v DKUM: 10.07.2015; Ogledov: 1483; Prenosov: 93
 Povezava na celotno besedilo |
5. Edge, vertex and mixed fault diametersIztok Banič, Rija Erveš, Janez Žerovnik, 2009, izvirni znanstveni članek Opis: Let ▫${mathcal{D}}^E_q(G)$▫ denote the maximum diameter among all subgraphs obtained by deleting ▫$q$▫ edges of ▫$G$▫. Let ▫${mathcal{D}}^V_p(G)$▫ denote the maximum diameter among all subgraphs obtained by deleting ▫$p$▫ vertices of ▫$G$▫. We prove that ▫${mathcal{D}}^E_a(G) leqslant {mathcal{D}}^V_a(G) + 1$▫ a for all meaningful ▫$a$▫. We also define mixed fault diameter ▫${mathcal{D}}^M_{(p,q)}(G)$▫, where ▫$p$▫ vertices and ▫$q$▫ edges are deleted at the same time. We prove that for ▫$0 < l leqslant a$▫, ▫${mathcal{D}}^E_a(G) leqslant {mathcal{D}}^M_{(a-ell,ell)}(G) leqslant {mathcal{D}}^V_a(G) + 1$▫, and give some examples.
Ključne besede: vertex-connectivity, edge-connectivity, vertex fault diameter, edge fault diameter, mixed fault diameter, interconnection network
Objavljeno v DKUM: 10.07.2015; Ogledov: 1321; Prenosov: 104
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6. Graphʼs theory approach for searching the shortest routing path in RIP protocol : a case studySaša Klampfer, Jože Mohorko, Žarko Čučej, Amor Chowdhury, 2012, izvirni znanstveni članek Opis: Routing is a problem domain with an infinite number of final-solutions. One of the possible approaches to solving such problems is using graph theory. This paper presents mathematical analysis methodologies based on circular graphs for solving a shortest path routing problem. The problem is focused on searching for the shortest path within a circular graph. Such a search coincides with the network routing problem domain. In this paper, we introduce in the detail all necessary parts needed to understand such an approach. This includes: definition of the routing problem domain, introduction to circular graphs and their usage, circular graphʼs properties, definition of walks through a circular graph, searching and determining the shortest path within a circular graph, etc. The state of the art routing methods, implemented in contemporary highly sophisticated routers, includes well-known weight-based algorithms and distance-vectors-based algorithms. The proposed solution can be placed between the two abovementioned methods. Each of these known methods strives for optimal results, but each of them also has its own deficiencies, which should be rectified with the proposed new method. This theoretically presented method is argued by a practical example and compared with the RIP (Routing Information Protocol) technique, where we look for the shortest path and possible walks through a specified circular graph.
Ključne besede: circular graphs, shortest path, graph diameter, walk through, CIGRP, connectivity matrix, network topology, symmetry, fully connected graph
Objavljeno v DKUM: 10.07.2015; Ogledov: 2265; Prenosov: 95
Povezava na celotno besedilo |
7. Edge, vertex and mixed fault-diametersIztok Banič, Rija Erveš, Janez Žerovnik, 2008 Opis: Let ▫${mathcal{D}}^E_q(G)$▫ denote the diameter of a graph ▫$G$▫ after deleting any of its ▫$q$▫ edges, and ▫${mathcal{D}}^V_p(G)$▫ denote the diameter of ▫$G$▫ after deleting any of its ▫$p$▫ vertices. We prove that ▫${mathcal{D}}^E_a(G) le {mathcal{D}}^V_a(G) + 1$▫ a for all meaningful ▫$a$▫. We also define mixed fault diameter ▫${mathcal{D}}^M_{(p,q)}(G)$▫, where ▫$p$▫ vertices and ▫$q$▫ edges are deleted at the same time. We prove that for ▫$0 < l le a$▫, ▫${mathcal{D}}^E_a(G) le {mathcal{D}}^M_{(a-l,l)}(G) le {mathcal{D}}^V_a(G) + 1$▫, and give some examples.
Ključne besede: matematika, teorija grafov, povezanost, mathematics, (vertex)-connectivity, edge-connectivity, (vertex) fault-diameter, edge-fault diameter, interconnection network
Objavljeno v DKUM: 10.07.2015; Ogledov: 1225; Prenosov: 93
Povezava na celotno besedilo |
8. Fault-diameter of Cartesian product of graphs and Cartesian graph bundlesIztok Banič, Janez Žerovnik, 2006 Opis: Cartesian graph bundles is a class of graphs that is a generalization of the Cartesian graph products. Let ▫$G$▫ be a ▫$k_G$▫-connected graph and ▫${mathcal{D}}_c(G)$▫ denote the diameter of ▫$G$▫ after deleting any of its ▫$c < k_G$▫ vertices. We prove that if ▫$G_1, G_2, dots, G_q$▫ are ▫$k_1$▫-connected, ▫$k_2$▫-connected,...,▫$k_q$▫-connected graphs and ▫$0 leq a_1 < k_1$▫, ▫$0 leq a_2 < k_2$▫,...,▫$0 leq a_q < k_q$▫ and ▫$a = a_1 + a_2 + dots + a_q + (q-1)$▫, then the fault diameter of ▫$G$▫, a Cartesian product of ▫$G_1$▫, ▫$G_2$▫,...,▫$G_q$▫, with ▫$a$▫ faulty nodes is ▫${mathcal{D}}_{a}(G) leq {mathcal{D}}_{a_1}(G_1)+{mathcal{D}}_{a_2}(G_2) + dots + {mathcal{D}}_{a_q}(G_q) + 1$▫. We also show that ▫${mathcal{D}}_{a+b+1}(G) leq {mathcal{D}}_a(F) + {mathcal{D}}_b(B) + 1$▫ if ▫$G$▫ is a graph bundle with fibre ▫$F$▫ over base ▫$B$▫, ▫$a leq k_F$▫, and ▫$b leq k_B$▫. As an auxiliary result we prove that connectivity of graph bundle ▫$G$▫ is at least ▫$k_F+k_B$▫.
Ključne besede: mathematics, graph theory, Cartesian graph bundles, Cartesian graph products, fault diameter, interconnection network
Objavljeno v DKUM: 10.07.2015; Ogledov: 1162; Prenosov: 34
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9. The strong isometric dimension of graphs of diameter twoJanja Jerebic, Sandi Klavžar, 2003 Opis: Krepka izometrična dimenzija ▫$textrm{idim}(G)$▫ grafa ▫$G$▫ je najmanjše število ▫$k$▫, za katero lahko ▫$G$▫ izometrično vložimo v krepki produkt ▫$k$▫ poti. Problem določitve ▫$textrm{idim}(G)$▫ za grafe premera dva je reduciran na problem pokrivanja komplementa grafa ▫$G$▫ s polnimi dvodelnimi grafi. Za primer je pokazano, da je izometrična dimenzija Petersenovega grafa enaka 5.
Ključne besede: matematika, teorija grafov, izometrični podgraf, krepki produkt grafov, premer grafa, krepka izometrična dimenzija, Petersenov graf, mathematics, graph theory, isometric subgraph, strong product of graphs, graph diameter, strong isometric dimension, Petersen graph
Objavljeno v DKUM: 10.07.2015; Ogledov: 1347; Prenosov: 48
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10. Wide diameter of Cartesian graph bundlesIztok Banič, Janez Žerovnik, 2010, objavljeni znanstveni prispevek na konferenci Opis: Fault tolerance and transmission delay of networks are important concepts in network design. The notions are strongly related to connectivity and diameter of a graph, and have been studied by many authors. Wide diameter of a graph combines studying connectivity with the diameter of a graph. Diameter with width ▫$k$▫ of a graph ▫$G$▫, ▫$k$▫-diameter, is defined as the minimum integer ▫$d$▫ for which there exist at least ▫$k$▫ internally disjoint paths of length at most ▫$d$▫ between any two distinct vertices in ▫$G$▫. Denote by ▫${mathscr D}_c(G)$▫ the ▫$c$▫-diameter of ▫$G$▫ and ▫$kappa(G)$▫ the connectivity of ▫$G$▫. In the context of computer networks, wide diameters of Cartesian graph products have been recently studied by many authors. Cartesian graph bundles is a class of graphs that is a generalization of the Cartesian graph products. Let ▫$G$▫ be a Cartesian graph bundle with fiber ▫$F$▫ over base ▫$B$▫, ▫$0 < a le kappa(F)$▫, and ▫$0 < b le kappa(B)$▫. We prove that ▫${mathscr D}_{a+b}(G) le {mathscr D}_a(F) + {mathscr D}_b(B) + 1$▫. Moreover, if ▫$G$▫ is a graph bundle with fiber ▫$F ne K_2$▫ over base ▫$B ne K_2$▫, then ▫${mathscr D}_{a+b}(G) le {mathscr D}_a(F) + {mathscr D}_b(B)$▫. The bounds are tight.
Ključne besede: mathematics, graph theory, Cartesian graph products, Cartesian graph bundles, wide diameter
Objavljeno v DKUM: 07.06.2012; Ogledov: 2043; Prenosov: 95
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