Independence number in graphs and its upper bounds - Farzad Shaveisi (Journal of Mahani Mathematical Research)
‎In this paper, we use the double counting method to find some upper bounds for the independence number of a simple graph in terms of its order, size and  maximum degree.   Moreover,  we determine extremal graphs attaining equality in upper bounds.  In addition, some lower bounds for the energy of graphs in terms of their size and maximum degree and the number of odd cycle, are determined.