On a conjecture of Murty and Simon on diameter two critical graphs II

Teresa W. Haynes; Michael A. Henning; Anders Yeo

doi:10.1016/j.disc.2011.09.022

On a conjecture of Murty and Simon on diameter two critical graphs II

Teresa W. Haynes, Michael A. Henning, Anders Yeo

Mathematics and Applied Mathematics

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

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 important association with total domination to prove the conjecture for the graphs whose complements have vertex connectivity k for k∈1,2,3.

Original language	English
Pages (from-to)	315-323
Number of pages	9
Journal	Discrete Mathematics
Volume	312
Issue number	2
DOIs	https://doi.org/10.1016/j.disc.2011.09.022
Publication status	Published - 28 Jan 2012

Keywords

Diameter 2-critical
Total domination edge critical
γ- critical

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/j.disc.2011.09.022

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On a conjecture of Murty and Simon on diameter two critical graphs II

Abstract

Keywords

ASJC Scopus subject areas

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