Computation of certain domination numbers of collaboration graphs

In this paper, a crisp overview is provided about the evolution of the concept of the collaboration graph resulting out of the social networks guided by the academic relation of coauthorship describing Erdos number. We have obtained some general results concerning the collaboration graph that evolves out of modeling the academic relationship among the Rolf Nevanlinna Prize winners based on their Erdos number. In addition, the strong and weak domination numbers and certain coloring numbers are also computed for the collaboration graph.