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1.
Povezavni, vozliščni in mešani okvarni premeri kartezičnih grafovskih produktov in svežnjev
Rija Erveš, 2011, dissertation

Abstract: V disertaciji raziskujemo povezanost in okvarne premere kartezičnih grafovskih svežnjev in kartezičnih produktov. Vpeljemo mešano povezanost in mešani okvarni premer grafa, ki posplošujeta povezanosti in okvarna premera definirana glede na eno vrsto okvarjenih elementov. Nekatere rezultate na kartezičnih grafovskih svežnjih in produktih glede na eno vrsto okvarjenih elementov posplošimo in v določenih primerih tudi izboljšamo.
Keywords: povezanost po vozliščih, povezanost po povezavah, mešana povezanost, okvarni premer, povezavni okvarni premer, mešani okvarni premer, kartezični grafovski sveženj, kartezični grafovski produkt, telekomunikacijska omrežja, okvarna toleranca
Published: 21.09.2011; Views: 3323; Downloads: 143
.pdf Full text (640,76 KB)

2.
Wide and fault diameters of Cartesian graph bundles
Janez Žerovnik, Iztok Banič, Rija Erveš, 2008, published scientific conference contribution abstract

Keywords: matematika, teorija grafov, kartezični produkt grafov
Published: 10.07.2015; Views: 247; Downloads: 8
URL Link to full text

3.
Edge, vertex and mixed fault-diameters
Iztok Banič, Rija Erveš, Janez Žerovnik, 2008

Abstract: 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.
Keywords: matematika, teorija grafov, povezanost, mathematics, (vertex)-connectivity, edge-connectivity, (vertex) fault-diameter, edge-fault diameter, interconnection network
Published: 10.07.2015; Views: 435; Downloads: 57
URL Link to full text

4.
Edge, vertex and mixed fault diameters
Iztok Banič, Rija Erveš, Janez Žerovnik, 2009, original scientific article

Abstract: 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.
Keywords: vertex-connectivity, edge-connectivity, vertex fault diameter, edge fault diameter, mixed fault diameter, interconnection network
Published: 10.07.2015; Views: 462; Downloads: 57
URL Link to full text

5.
The edge fault-diameter of Cartesian graph bundles
Iztok Banič, Rija Erveš, Janez Žerovnik, 2009, original scientific article

Abstract: 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 ▫$k_F + k_B$▫.
Keywords: matematika, teorija grafov, kartezični grafovski produkti, kartezični grafovski svežnji, povezavni okvarni premer, mathematics, graph theory, Cartesian graph products, Cartesian graph bundles, edge-fault diameter
Published: 10.07.2015; Views: 566; Downloads: 56
URL Link to full text

6.
On vulnerability measures of networks
Rija Erveš, Darja Rupnik Poklukar, Janez Žerovnik, 2013, published scientific conference contribution

Abstract: As links and nodes of interconnection networks are exposed to failures, one of the most important features of a practical networks design is fault tolerance. Vulnerability measures of communication networks are discussed including the connectivities, fault diameters, and measures based on Hosoya- Wiener polynomial. An upper bound for the edge fault diameter of product graphs is proved.
Keywords: discrete optimization, communication network, vulnerability
Published: 21.07.2017; Views: 320; Downloads: 63
.pdf Full text (189,03 KB)
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7.
VARNOSTNI FAKTORJI IN TEHNIČNE LASTNOSTI DIRKALNEGA VOZILA V IZREDNIH OKOLIŠČINAH
Gregor Divjak, 2014, undergraduate thesis

Abstract: Diplomsko nalogo smo razdelili na tri dele. V prvem delu bomo preverili potrebna pooblastila in dovoljenja za izvedbo športnega dogodka, kjer bi postavili nov svetovni rekord. V tehnično-varnostnem delu bomo pogledali tehnične lastnosti reli vozila in rampe. V računskem delu bomo preverili izračune, ali je pravzaprav sploh možno še izboljšati trenutni rekord. Ugotovili smo, da je v Sloveniji možno izvesti takšen dogodek z vsemi potrebnimi dovoljenji in pooblastili. Izračuni so pokazali, da je možna izboljšava trenutnega rekorda, žal pa takšnega projekta ne moremo izpeljati samo, saj nimamo dovolj finančnih sredstev.
Keywords: skok, tehnične lastnosti, varnostni faktorji, dirkalno vozilo, organizacija, izračuni, dirkač.
Published: 10.11.2014; Views: 988; Downloads: 70
.pdf Full text (3,88 MB)

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