Title
Progress on the Murty–Simon Conjecture on Diameter-2 Critical Graphs: A Survey
Document Type
Article
Publication Date
10-1-2015
Description
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.
Citation Information
Haynes, Teresa W.; Henning, Michael A.; van der Merwe, Lucas C.; and Yeo, Anders. 2015. Progress on the Murty–Simon Conjecture on Diameter-2 Critical Graphs: A Survey. Journal of Combinatorial Optimization. Vol.30(3). 579-595. https://doi.org/10.1007/s10878-013-9651-7 ISSN: 1382-6905