Iztok Banič (Author), Rija Erveš (Author), Janez Žerovnik (Author)

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;

Data

Language: English
Year of publishing:
Typology: 1.01 - Original Scientific Article
Organization: UL FS - Faculty of Mechanical Engineering
UDC: 519.17
COBISS: 15145817 Link will open in a new window
ISSN: 0195-6698
Views: 43
Downloads: 26
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Other data

Secondary language: Slovenian
Secondary title: Povezavni okvarni premer kartezičnih svežnjev
Secondary abstract: A Cartesian graph bundle is a generalization of a graph covering and a Cartesian graph product. Let ▫$G$▫ be a ▫$k_G$▫-edge connected graph and ▫${\bar{\mathcal{D}}_c(G)}$▫ be the largest diameter of subgraphs of ▫$G$▫ obtained by deleting ▫$c < k_G$▫ edges. We prove that ▫${\bar{\mathcal{D}}_{a+b+1}(G)} \le {\bar{\mathcal{D}}_a(F)} \le {\bar{\mathcal{D}}_b(B)} + 1$▫ if ▫$G$▫ is a graph bundle with fibre ▫$F$▫ over base $B$, ▫$a < k_F$▫, and ▫$b<k_B$▫. As an auxiliary result we prove that the edge-connectivity of graph bundle ▫$G$▫ is at least ▫$k_F + k_B$▫.
Secondary keywords: matematika;teorija grafov;kartezični grafovski produkti;kartezični grafovski svežnji;povezavni okvarni premer;
URN: URN:SI:UM:
Type (COBISS): Not categorized
Pages: str. 1054-1061
Volume: ǂVol. ǂ30
Issue: ǂno. ǂ5
Chronology: 2009
ID: 1474266