G-2005-08
Automated Results and Conjectures on Average Distance in Graphs
et référence BibTeX
Using the AutoGraphiX 2 system, a systematic study is made on generation and proof of relations of the form
where $\overline{l}$ denotes the average distance between distinct vertices of a connected graph G, i one of the invariants: diameter, radius, girth, maximum, average and minimum degree, $\underline{b}n$ and $\overline{b}n$ are best possible lower and upper bounds, functions of the order n of G and $\oplus \in { -,+ \times, /}$. In 24 out of 48 cases simple bounds are obtained and proved by the system. In 21 more cases, the system provides bounds, 16 of which are proved by hand.
Paru en janvier 2005 , 23 pages
Ce cahier a été révisé en novembre 2005
Axes de recherche
Applications de recherche
Publication
jan. 2007
Automated results and conjectures on average distance in graph
et
J.A. Bondy, J. Fonlupt, J.L. Fouquet, J.C. Fournier, L. Ramirez-Alfonsin (eds.), Game Theory in Paris: Special Volume in Memory of Claude Berge, 21–36, 2007
référence BibTeX