Groupe d’études et de recherche en analyse des décisions

G-2008-36

Nordhaus-Gaddum Relations for Proximity and Remoteness in Graphs

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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