Nordhaus-Gaddum relations for proximity and remoteness in graphs

Authors:
M. Aouchiche;P. Hansen
Affiliations:
GERAD and HEC Montreal, Montreal, QC, Canada;GERAD and HEC Montreal, Montreal, QC, Canada
Venue:
Computers & Mathematics with Applications
Year:
2010

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Abstract

The transmission of a vertex in a connected graph is the sum of all distances from that vertex to the others. It is said to be normalized if divided by n-1, where n denotes the order of the graph. The proximity of a graph is the minimum normalized transmission, while the remoteness is the maximum normalized transmission. In this paper, we give Nordhaus-Gaddum-type inequalities for proximity and remoteness in graphs. The extremal graphs are also characterized for each case.