A Proof of a Conjecture on Diameter 2-Critical Graphs Whose Complements Are Claw-Free

Creator(s)

Teresa W. Haynes, East Tennessee State UniversityFollow
Michael A. Henning, University of Johannesburg
Anders Yeo, Royal Holloway, University of London

Document Type

Article

Publication Date

8-1-2011

Description

A graph G is diameter 2-critical if its diameter is 2, 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 n24 and that the extremal graphs are complete bipartite graphs with equal size partite sets. We use an important association with total domination to prove the conjecture for the graphs whose complements are claw-free.

Citation Information

Haynes, Teresa W.; Henning, Michael A.; and Yeo, Anders. 2011. A Proof of a Conjecture on Diameter 2-Critical Graphs Whose Complements Are Claw-Free. Discrete Optimization. Vol.8(3). 495-501. https://doi.org/10.1016/j.disopt.2011.04.003 ISSN: 1572-5286