Groupe d’études et de recherche en analyse des décisions

# Nordhaus-Gaddum Relations for Proximity and Remoteness in Graphs

## Mustapha Aouchiche et Pierre Hansen

The transmission of a vertex in a connected graph is the sum of all distance 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 the proximity and remoteness in graphs. The extremal graphs are also characterize for each case.

, 17 pages