| Title: | Wide diameter of Cartesian graph bundles |
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| Authors: | ID Banič, Iztok (Author)
ID Žerovnik, Janez (Author) |
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| Files: |  http://dx.doi.org/10.1016/j.disc.2009.11.024
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| Language: | English |
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| Work type: | Article |
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| Typology: | 1.08 - Published Scientific Conference Contribution |
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| Organization: | FNM - Faculty of Natural Sciences and Mathematics
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| Abstract: | Fault tolerance and transmission delay of networks are important concepts in network design. The notions are strongly related to connectivity and diameter of a graph, and have been studied by many authors. Wide diameter of a graph combines studying connectivity with the diameter of a graph. Diameter with width ▫$k$▫ of a graph ▫$G$▫, ▫$k$▫-diameter, is defined as the minimum integer ▫$d$▫ for which there exist at least ▫$k$▫ internally disjoint paths of length at most ▫$d$▫ between any two distinct vertices in ▫$G$▫. Denote by ▫${mathscr D}_c(G)$▫ the ▫$c$▫-diameter of ▫$G$▫ and ▫$kappa(G)$▫ the connectivity of ▫$G$▫. In the context of computer networks, wide diameters of Cartesian graph products have been recently studied by many authors. Cartesian graph bundles is a class of graphs that is a generalization of the Cartesian graph products. Let ▫$G$▫ be a Cartesian graph bundle with fiber ▫$F$▫ over base ▫$B$▫, ▫$0 < a le kappa(F)$▫, and ▫$0 < b le kappa(B)$▫. We prove that ▫${mathscr D}_{a+b}(G) le {mathscr D}_a(F) + {mathscr D}_b(B) + 1$▫. Moreover, if ▫$G$▫ is a graph bundle with fiber ▫$F ne K_2$▫ over base ▫$B ne K_2$▫, then ▫${mathscr D}_{a+b}(G) le {mathscr D}_a(F) + {mathscr D}_b(B)$▫. The bounds are tight. |
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| Keywords: | mathematics, graph theory, Cartesian graph products, Cartesian graph bundles, wide diameter |
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| Year of publishing: | 2010 |
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| PID: | 20.500.12556/DKUM-35459  |
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| UDC: | 519.17 |
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| ISSN on article: | 0012-365X |
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| COBISS.SI-ID: | 17543176 |
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| NUK URN: | URN:SI:UM:DK:OLXAAPZ0 |
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| Publication date in DKUM: | 07.06.2012 |
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| Views: | 2265 |
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| Downloads: | 98 |
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| Metadata: |    |
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| Categories: | Misc.
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