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The maximum number of edges in a minimal graph of diameter 2
Author(s) -
Füredi Zoltán
Publication year - 1992
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.3190160110
Subject(s) - combinatorics , mathematics , bipartite graph , conjecture , graph , complete bipartite graph , crossing number (knot theory) , discrete mathematics , intersection (aeronautics) , engineering , aerospace engineering
A graph g of diameter 2 is minimal if the deletion of any edge increases its diameter. Here the following conjecture of Murty and Simon is proved for n < n o . If g has n vertices then it has at most n 2 /4 edges. The only extremum is the complete bipartite graph.