| Title: | Fault-diameter of Cartesian product of graphs and Cartesian graph bundles |
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| Authors: | ID Banič, Iztok (Author)
ID Žerovnik, Janez (Author) |
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| Files: |  http://www.imfm.si/preprinti/PDF/01016.pdf
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| Language: | English |
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| Work type: | Not categorized |
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| Organization: | FS - Faculty of Mechanical Engineering
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| Abstract: | 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 ▫$k_F+k_B$▫. |
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| Keywords: | mathematics, graph theory, Cartesian graph bundles, Cartesian graph products, fault diameter, interconnection network |
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| Year of publishing: | 2006 |
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| Number of pages: | str. 1-17 |
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| Numbering: | Vol. 44, št. 1016 |
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| PID: | 20.500.12556/DKUM-49377  |
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| ISSN: | 1318-4865 |
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| UDC: | 519.17 |
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| COBISS.SI-ID: | 14564441 |
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| NUK URN: | URN:SI:UM:DK:FUEL9SZJ |
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| Publication date in DKUM: | 10.07.2015 |
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| Views: | 1327 |
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| Downloads: | 59 |
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| Metadata: |    |
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| Categories: | Misc.
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