Let X = {x1, ., x,,,} and Y= { J'~,. ,y,,\_} be two disjoint sets of vertices in a graph G. Then (X, Y) is called an antipodal set-pair ofsize m (m-ASP, for short) if the distance of xi and yj is at most two if and only if i #j. We prove that in a graph of maximum degree k every m-ASP has size m < k
Fairness, distances and degrees
β Scribed by Philippe Darondeau; Doris Nolte; Lutz Priese; Serge Yoccoz
- Publisher
- Elsevier Science
- Year
- 1992
- Tongue
- English
- Weight
- 775 KB
- Volume
- 97
- Category
- Article
- ISSN
- 0304-3975
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
We prove that in a graph of order n and minimum degree d, the mean distance Β΅ must satisfy This asymptotically confirms, and improves, a conjecture of the computer program GRAFFITI. The result is close to optimal; examples show that for any d, Β΅ may be larger than n/(d + 1).
95-99 mistakenly attributes the computer program GRAFFITI to Fajtlowitz and Waller, instead of just Fajtlowitz. (Our apologies to Siemion Fajtlowitz.) Note also that one of the ''flaws'' we note for Conjecture 62 (that it was made for graphs regular of degree d, vice graphs of minimum degree d) was
The average distance Β΅(G) of a connected graph G of order n is the average of the distances between all pairs of vertices of G, i.e., Β΅(G) = ( n 2 ) -1 {x,y}βV (G) d G (x, y), where V (G) denotes the vertex set of G and d G (x, y) is the distance between x and y. We prove that every connected graph