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Average distance and domination number

✍ Scribed by P. Dankelmann

Book ID
104294820
Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
846 KB
Volume
80
Category
Article
ISSN
0166-218X

No coin nor oath required. For personal study only.

✦ Synopsis

We give a sharp upper bound on the average distance of a graph of given order and domination number and determine the extremal graphs.

πŸ“œ SIMILAR VOLUMES

The average distance and the independenc
The average distance and the independence number
✍ F. R. K. Chung πŸ“‚ Article πŸ“… 1988 πŸ› John Wiley and Sons 🌐 English βš– 258 KB

We prove that in every connected graph the independence number is at least as large as the average distance between vertices. Theorem. For every connected graph G , we have a ( G ) 2 D ( G ) , with equality if and only if G is a complete graph.