Maximum edges possible in a graph for restricted independence number,   maximum degree, and maximum matching size
  This article provides sharp bounds for the maximum number of edges possible in a simple graph with restricted values of two of the three parameters, namely, maxi- mum matching size, independence number and maximum degree. We also construct extremal graphs that achieve the edge bounds in all cases. We further establish uniqueness of these extremal graphs whenever they are unique. 
Niraj Khare, Nishali Mehta, Naushad Puliyambalath
math.CO