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Mean distance and minimum degree
Author(s) -
Kouider Mekkia,
Winkler Peter
Publication year - 1997
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/(sici)1097-0118(199705)25:1<95::aid-jgt7>3.0.co;2-d
Subject(s) - mathematics , conjecture , combinatorics , degree (music) , graph , minimum distance , order (exchange) , discrete mathematics , graph theory , economics , physics , acoustics , finance
Abstract We prove that in a graph of order n and minimum degree d, the mean distance μ must satisfy $$\mu \leq {{n}\over{d+1}} \,+ 2.$$ .This asymptotically confirms, and improves, a conjecture of the computer program GRAFFITI. The result is close to optimal; examples show that for any d, μ may be larger than n /( d + 1). © 1997 John Wiley & Sons, Inc. J Graph Theory 25: 95–99, 1997