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Diameter-critical graphs

✍ Scribed by N. P. Khomenko; N. A. Ostroverkhii


Book ID
112478582
Publisher
Springer
Year
1971
Tongue
English
Weight
556 KB
Volume
22
Category
Article
ISSN
0041-5995

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πŸ“œ SIMILAR VOLUMES


On diameter critical graphs
✍ Louis Caccetta; Roland HΓ€ggkvist πŸ“‚ Article πŸ“… 1979 πŸ› Elsevier Science 🌐 English βš– 520 KB
On diameter 2-critical graphs
✍ Genghua Fan πŸ“‚ Article πŸ“… 1987 πŸ› Elsevier Science 🌐 English βš– 296 KB

A graph is diameter 2-critical if the graph has diameter 2 and the deletion of any edge increases its diameter. We prove that if G is diameter 2-critical graph on n vertices and e edges, then (i) e ~< [14n2 ] for n <~ 24, and (ii) e < !4n2 + (n 2 -16.2 n + 56)/320 (<0.2532 n2), for n/> 25.

Minimum vertex-diameter-2-critical graph
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## Abstract We prove that the minimum number of edges in a vertex‐diameter‐2‐critical graph on __n__ β‰₯ 23 vertices is (5__n__β€‰βˆ’β€‰17)/2 if __n__ is odd, and is (5__n__/2)β€‰βˆ’β€‰7 if __n__ is even. Β© 2005 Wiley Periodicals, Inc. J Graph Theory

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## Abstract A graph is __k__‐domination‐critical if Ξ³(__G) = k__, and for any edge __e__ not in __G__, Ξ³(__G + e) = k__ βˆ’ 1. In this paper we show that the diameter of a domination __k__‐critical graph with __k__ ≧ 2 is at most 2__k__ βˆ’ 2. We also show that for every __k__ ≧ 2, there is a __k__‐dom