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On a conjecture of Murty and Simon on diameter 2-critical graphs |
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| Authors: | Teresa W Haynes Michael A Henning Lucas C van der Merwe Anders Yeo |
| Institution: | aDepartment of Mathematics, East Tennessee State University, Johnson City, TN 37614-0002, USA;bDepartment of Mathematics, University of Johannesburg, Auckland Park 2006, South Africa;cDepartment of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37403, USA;dDepartment of Computer Science, Royal Holloway, University of London, Egham, Surrey, TW20 OEX, UK |
| Abstract: | A graph 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 of order n is at most n2/4 and that the extremal graphs are complete bipartite graphs with equal size partite sets. We use an association with total domination to prove the conjecture for the graphs whose complements have diameter three. |
| Keywords: | Diameter critical Total domination edge critical |
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