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Locally geodesic cycles in 2-self-centered graphs

✍ Scribed by Seiya Negami; Guang-Han Xu

Publisher
Elsevier Science
Year
1986
Tongue
English
Weight
333 KB
Volume
58
Category
Article
ISSN
0012-365X

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✦ Synopsis

A cycle C in G is said to be locally geodesic at a vertex v if for each vertex u on C, the distance between v and u in C coincides with that in G. It will be shown that a self-centered graph of radius 2 contains a cycle of length 4 or 5 which is locally geodesic at each vertex and conversely that if the longest one among such cycles for each vertex of a block has length 4 then the block is self-centered and has radius 2.

πŸ“œ SIMILAR VOLUMES

Geodesics and almost geodesic cycles in
Geodesics and almost geodesic cycles in random regular graphs
✍ Itai Benjamini; Carlos Hoppen; Eran Ofek; PaweΕ‚ PraΕ‚at; Nick Wormald πŸ“‚ Article πŸ“… 2010 πŸ› John Wiley and Sons 🌐 English βš– 198 KB

A geodesic in a graph G is a shortest path between two vertices of G. For a specific function e(n) of n, we define an almost geodesic cycle C in G to be a cycle in which for every two vertices u and v in C, the distance d G (u, v) is at least d C (u, v)-e(n). Let (n) be any function tending to infin