The Sum and Product of Chromatic Numbers of Graphs and their Line Graphs
  A Nordhaus-Gaddum-type result is a (tight) lower or upper bound on the sum or product of a parameter of a graph and its complement. In this paper some variations are considered. First, recall their theorem, which gives bounds on the sum and the product of the chromatic number of a graph with that of its complement. In this paper, we provide a new characterization of the other class of graphs. 
Sunny Joseph Kalayathankal and Susanth C
math.CO