A proof of the conjecture regarding the sum of domination number and average eccentricity

The average eccentricity ecc(G)ecc(G) of a graph GG is the mean value of eccentricities of all vertices of GG. In this paper, we continue the work of Ilić (2012) and resolve a conjecture, obtained by the system AutoGraphiX, about the upper bound on the sum of the average eccentricity and the domination number among connected graphs on nn vertices.