Iskanje po katalogu digitalne knjižnice

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: 320; Prenosov: 14
Povezava na celotno besedilo

Opis: Grafovski svežnji predstavljajo posplošitev krovnih in produktnih grafov. V članku vpeljemo enolično lokalno produktno relacijo ▫$Delta$▫ na kartezičnih svežnjih nad baznimi grafi, ki ne vsebujejo grafa ▫$K_4 setminus e$▫ in podamo algoritem za razpoznavanje kartezičnih svežnjev nad enostavnimi baznimi grafi brez ▫$K_4 setminus e$▫.
Ključne besede: matematika, teorija grafov, kartezični grafovski svežnji, enolična lokalna produktna lastnost, osnovna faktorizacija, razpoznavanje, polinomski algoritem, mathematics, graph theory, Cartesian graph bundles, unique square property, fundamental factorization, polynomial algorithm, recognition
Objavljeno: 10.07.2015; Ogledov: 295; Prenosov: 45
Povezava na celotno besedilo

Opis: In this paper we show that methods for recognizing Cartesian graph bundles can be generalized to weighted digraphs. The main result is an algorithm which lists the sets of degenerate arcs for all representations of digraph as a weighted directed Cartesian graph bundle over simple base digraphs not containing transitive tournament on three vertices. Two main notions are used.The first one is the new relation ▫$\vec{\delta}^\ast$▫ defined among the arcs of a digraph as a weighted directed analogue of the well-known relation ▫$\delta^\ast$▫. The second one is the concept of half-convex subgraphs. A subgraph ▫$H$▫ is half-convex in ▫$G$▫ if any vertex ▫$x \in G \setminus H$▫ has at most one predecessor and at most one successor
Ključne besede: mathematics, graph theory, graph bundles, Cartesian graph product, weighted digraphs, half-convexity
Objavljeno: 31.03.2017; Ogledov: 333; Prenosov: 163
Celotno besedilo (240,86 KB)
Gradivo ima več datotek! Več...