A graph $$G$$G is diameter 2-critical if its diameter is two and the deletion of any edge increases the diameter. Murty and Simon conjectured that the number of edges in a diameter-2-critical graph G of order n is at most ⌊n2/4⌋ and that the extremal graphs are the complete bipartite graphs K⌊n/2⌋,⌈n/2⌉. We survey the progress made to date on this conjecture, concentrating mainly on recent results developed from associating the conjecture to an equivalent one involving total domination.
| Identifer | oai:union.ndltd.org:ETSU/oai:dc.etsu.edu:etsu-works-16647 |
| Date | 01 October 2015 |
| Creators | Haynes, Teresa W., Henning, Michael A., van der Merwe, Lucas C., Yeo, Anders |
| Publisher | Digital Commons @ East Tennessee State University |
| Source Sets | East Tennessee State University |
| Detected Language | English |
| Type | text |
| Source | ETSU Faculty Works |
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