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.
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© 2003 Springer-Verlag Berlin Heidelberg
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Manuel, P., Rajan, B., Rajasingh, I., Alaguvel, A. (2003). Tree Spanners, Cayley Graphs, and Diametrically Uniform Graphs. In: Bodlaender, H.L. (eds) Graph-Theoretic Concepts in Computer Science. WG 2003. Lecture Notes in Computer Science, vol 2880. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39890-5_29
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DOI: https://doi.org/10.1007/978-3-540-39890-5_29
Publisher Name: Springer, Berlin, Heidelberg
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