SLO | ENG | Piškotki in zasebnost

Večja pisava | Manjša pisava

Iskanje po katalogu digitalne knjižnice Pomoč

Iskalni niz: išči po
išči po
išči po
išči po
* po starem in bolonjskem študiju

Opcije:
  Ponastavi


1 - 5 / 5
Na začetekNa prejšnjo stran1Na naslednjo stranNa konec
1.
2.
Fault-diameter of Cartesian product of graphs and Cartesian graph bundles
Iztok 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: 10.07.2015; Ogledov: 308; Prenosov: 12
URL Povezava na celotno besedilo

3.
Edge, vertex and mixed fault-diameters
Iztok 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: 10.07.2015; Ogledov: 280; Prenosov: 30
URL Povezava na celotno besedilo

4.
Edge, vertex and mixed fault diameters
Iztok 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: 10.07.2015; Ogledov: 353; Prenosov: 23
URL Povezava na celotno besedilo

5.
The edge fault-diameter of Cartesian graph bundles
Iztok 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: 10.07.2015; Ogledov: 378; Prenosov: 24
URL Povezava na celotno besedilo

Iskanje izvedeno v 0.14 sek.
Na vrh
Logotipi partnerjev Univerza v Mariboru Univerza v Ljubljani Univerza na Primorskem Univerza v Novi Gorici