Abstract
In line with symmetrical graphs such as Cayley graphs and vertex transitive graphs, we introduce a new class of symmetrical graphs called diametrically uniform graphs. The class of diametrically uniform graphs includes vertex transitive graphs and hence Cayley graphs. A tree t-spanner of graph G is a spanning tree T in which the distance between every pair of vertices is at most t times their distance in G. The minimum tree spanner problem of a graph G is to find a tree t-spanner with t as small as possible. In this paper, the minimum tree spanner problem is exhaustively studied for diametrically uniform graphs, which also include 3-regular mesh of trees and generalized Petersen graphs.KeywordsMinimum Tree SpannerCayley GraphParallel ArchitectureSpan SubgraphPetersen GraphThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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