There are occasions when an average value of a graph parameter gives more useful information than the basic global value. In this paper, we introduce the concept of the average covering number of a graph (the covering number of a graph is the minimum number of vertices in a set with the property that every edge has a vertex in the set). We establish relationships between the average covering number and some other graph parameters, find the extreme values of the average covering number among all graphs of a given order, and find the average covering number for some families of graphs.
Derya Dogan. Pinar Dundar. "The Average Covering Number of a Graph." J. Appl. Math. 2013 1 - 4, 2013. https://doi.org/10.1155/2013/849817