Progress on the Murty–Simon Conjecture on Diameter-2 Critical Graphs: A Survey

Creator(s)

Teresa W. Haynes, East Tennessee State UniversityFollow
Michael A. Henning, University of Johannesburg
Lucas C. van der Merwe, University of Tennessee at Chattanooga
Anders Yeo, University of Johannesburg

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