Diameter and Broadcast Time of the Knödel graph

Efficient dissemination of information remains a central challenge for all types of networks. There are two ways to handle this issue. One way is to compress the amount of data being transferred and the second way is to minimize the delay of information distribution. Well-received approaches used in the second way either design efficient algorithms or implement reliable network architectures with optimal dissemination time. Among the well-known network architectures, the Knödel graph can be considered a suitable candidate for the problem of information dissemination. The Knödel graph W_(d, n) is a regular graph, of an even order n and degree d, 1 ≤ d ≤ floor(log n). The Knödel graph was introduced by W. Knödel almost four decades ago as network architecture with good properties in terms of broadcasting and gossiping in interconnected networks. Although the Knödel graph has a highly symmetric structure, its diameter is only known for W_(d, 2^d). Recently, the general upper and lower bounds on diameter and broadcast time of the Knödel graph have been presented. In this thesis, our motivation is to find the diameter, the number of vertices at a particular distance and the broadcast time of the Knödel graph. Theoretically, we succeed to prove the diameter and the broadcast time of the Knödel graph W_(3, n). We also claim that the Knödel graph W_(3, n) for n = 4 mod 4 and n > 16, is a diametral broadcast graph. We present that W_(3, 22) is a broadcast graph. Experimentally, however, we obtain the following results; (a) the diameter of some specific Knödel graphs, and (b) the propositions on the number of vertices at a particular distance. We also construct a new graph, denoted as HW_(d,2^d), by connecting Knödel graph W_(d-1,2^(d-1)) to hypercube H_(d-1) and experimentally show that HW_(d,2^d) has even a smaller diameter than Knödel graph W_(d,2^d)

Local site seismic response in an alpine valley: seismic microzonation of the Castel Caldes area (North-western Trentino)

The purpose of this work is to analyse the local-site seismic response in the Castel Caldes area, located in an alpine valley (Val di Sole) of the north-western Trentino region. The final result is the seismic microzonation map of this area. The seismic microzonation aims to characterize at a small scale two contiguous localities in which the seismic motion is amplified (and how), due to the lithostratigraphic and geomorphological specific characteristicsope

A NOTE ON THE DIMENSIONALITY OF MODIFIED KNÖDEL GRAPHS

International audienceWe show that the edges of the modi ed Kn odel graph can be grouped into dimensions which are similar to the dimensions of hypercubes. In particular, routing, broadcasting and gossiping, can be done easily in modi ed Kn odel graphs using these dimensions

Feedback Numbers of Goldberg Snark, Twisted Goldberg Snarks and Related Graphs

A subset of vertices of a graph G is called a feedback vertex set of G if its removal results in an acyclic subgraph. The minimum cardinality of a feedback vertex set is called the feedback number. In this paper, we determine the exact values of the feedback numbers of the Goldberg snarks Gn and its related graphs Gn*, Twisted Goldberg Snarks TGn and its related graphs TGn*. Let f(n) denote the feedback numbers of these graphs, we prove that f(n)=2n+1, for n≥3

Glaze visualization framework for mobile devices

Supervisor: Ian Oakle