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

The average eccentricity e c c ( G ) of a graph G is the mean value of eccentricities of all vertices of G . In this paper, we continue the work of Ilic (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 n vertices.