A graph G is diameter-2-critical if its diameter is two and the deletion of any edge increases the diameter. In this paper we characterize the diameter-2-critical graphs with no antihole of length four, that is, the diameter-2-critical graphs whose complements have no induced 4-cycle. Murty and Simon conjectured that the number of edges in a diameter-2-critical graph of order n is at most n 2/4 and that the extremal graphs are complete bipartite graphs with equal size partite sets. As a consequence of our characterization, we prove the Murty-Simon Conjecture for graphs with no antihole of length four.
Identifer | oai:union.ndltd.org:ETSU/oai:dc.etsu.edu:etsu-works-17516 |
Date | 01 June 2012 |
Creators | Haynes, Teresa W., Henning, Michael A. |
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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