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

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.

Identiferoai:union.ndltd.org:ETSU/oai:dc.etsu.edu:etsu-works-17854
Date01 August 2011
CreatorsHaynes, Teresa W., Henning, Michael A., Yeo, Anders
PublisherDigital Commons @ East Tennessee State University
Source SetsEast Tennessee State University
Detected LanguageEnglish
Typetext
SourceETSU Faculty Works

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