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The Global ETD Search service is a free service for researchers
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Distance Consistent Labellings and the Local List NumberHenricsson, Anders January 2023 (has links)
We study the local list number of graphs introduced by Lennerstad and Eriksson. A labelling of a graph on n vertices is a bijection from vertex set to the set {1,…, n}. Given such a labelling c a vertex u is distance consistent if for all vertices v and w |c(u)-c(v)|=|c(u)-c(w)|+1 implies d(u,w)≤ d(u,v). A graph G is k-distance consistent if there is a labelling with k distance-consistent vertices. The local list number of a graph G is the largest k such that G is k-distance consistent. We determine the local list number of cycles, complete bipartite graphs and some trees as well as prove bounds for some families of trees. We show that the local list number of even cycles is two, and of odd cycles is three. We also show that, if k, l≥ 3 , the complete bipartite graph Kk,l has local list number one, the star graph Sn=K1,n has local list number 3, and K2,k has local list number 2. Finally, we show that for each n≥3 and each k such that 3≤k≤n there is a tree with local list number k. / Vi studerar det lokala listtalet introducerat av Lennerstad och Eriksson. En märkning av en graf på n hörn är en bijektion från hörnmängden till mängden {1, . . . , n}. Givet en sådan märkning c är ett hörn u avståndskonsistent om för alla hörn v och w |c(u) − c(v)| = |c(u) − c(w)| = 1 implicerar d(u, w) ≤d(u, v). En graf G är k-avståndskonsistent om det nns en märkning med k avståndskonsistenta hörn. Det lokala listtalet av en graf G är det största k sådan att G är k -avståndskonsistent. Vi bestämmer den lokala listtalet av cykler, kompletta bipartita grafer och vissa träd och visar som gränser för några familjer av träd. Vi visar att det lokla listtalet av jämna cykler är två, och av udda cykler är tre. Vi visar också att, om k, l ≥ 3, den kompletta bipartita grafen Kk,l har lokalt listtal ett, stjärngrafen Sn = K1,n har lokalt listtal 3, och K2,k har lokalt listtal 2. Slutligen, visar vi att för varje n≥3 och varje k sådant att 3 ≤ k≤n finns ett träd med lokalt listtal k.
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Fault Location Algorithms in Transmission GridsHarrysson, Mattias January 2014 (has links)
The rapid growth of the electric power system has in recent decades resulted in an increase of the number of transmission lines and total power outage in Norway. The challenge of a fast growing electrical grid has also resulted in huge increases of overhead lines and their total length. These lines are experiencing faults due to various reasons that cause major disruptions and operating costs of the transmission system operator (TSO). Thus, it’s important that the location of faults is either known or can be estimated with reasonably high accuracy. This allows the grid owner to save money and time for inspection and repair, as well as to provide a better service due to the possibility of faster restoration of power supply and avoiding blackouts. Fault detection and classification on transmission lines are important tasks in order to protect the electrical power system. In recent years, the power system has become more complicated under competitive and deregulated environments and a fast fault location technique is needed to maintain security and supply in the grid. This thesis compares and evaluates different methods for classification of fault type and calculation of conventional one-side and two-side based fault location algorithms for distance to fault estimation. Different algorithm has been implemented, tested and verified to create a greater understanding of determinants facts that affect distance to faults algorithm’s accuracy. Implemented algorithm has been tested on the data generated from a number of simulations in Simulink for a verification process in implemented algorithms accuracy. Two types of fault cases have also been simulated and compared for known distance to fault estimation.
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