Nordhaus–Gaddum relations for proximity and remoteness in graphs

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−1n−1, where nn 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.