The average distance p(G) of a graph G is the average among the distances between all pairs of vertices in G. For n 2 2, the average Steiner n-distance ,4G) of a connected graph G is the average Steiner distance over all sets of n vertices in G. It is shown that for a connected weighted graph G, pu,
Computing the average distance of an interval graph
β Scribed by Peter Dankelmann
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 306 KB
- Volume
- 48
- Category
- Article
- ISSN
- 0020-0190
No coin nor oath required. For personal study only.
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## Abstract A graph __G__ with maximum degree Ξ and edge chromatic number $\chi\prime({G}) > \Delta$ is __edge__βΞβ__critical__ if $\chi\prime{(G-e)} = \Delta$ for every edge __e__ of __G__. It is proved that the average degree of an edgeβΞβcritical graph is at least ${2\over 3}{(\Delta+1)}$ if $\D