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Edge-vulnerability and mean distance

✍ Scribed by Odile Favaron; Mekkia Kouider; Maryvonne Mahéo

Publisher
John Wiley and Sons
Year
1989
Tongue
English
Weight
450 KB
Volume
19
Category
Article
ISSN
0028-3045

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📜 SIMILAR VOLUMES

Mean distance and minimum degree
Mean distance and minimum degree
✍ Kouider, Mekkia; Winkler, Peter 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 80 KB

We prove that in a graph of order n and minimum degree d, the mean distance µ 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, µ may be larger than n/(d + 1).

Erratum: Mean distance and minimum degre
Erratum: Mean distance and minimum degree
✍ Kouider, Mekkia; Winkler, Peter 📂 Article 📅 1999 🏛 John Wiley and Sons 🌐 English ⚖ 86 KB

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

Properties of edge-deleted distance stab
Properties of edge-deleted distance stable graphs
✍ Klemm, Karen; Winters, Steven J. 📂 Article 📅 1999 🏛 John Wiley and Sons 🌐 English ⚖ 72 KB 👁 2 views

The distance from a vertex u to a vertex v in a connected graph G is the length of a shortest u-v path in G. The distance of a vertex v of G is the sum of the distances from v to the vertices of G. For a vertex v in a 2-edge-connected graph G, we define the edge-deleted distance of v as the maximum