On solving a non-convex quadratic programming problem involving resistance distances in graphs

Quadratic programming problems involving distance matrix ( D ) that arises in trees are considered in the literature by Dankelmann (Discrete Math 312:12–20, 2012 ), Bapat and Neogy (Ann Oper Res 243:365–373, 2016 ). In this paper, we consider the question of solving the quadratic programming problem of finding maximum of x T R x subject to x being a nonnegative vector with sum 1 and show that for the class of simple graphs with resistance distance matrix ( R ) which are not necessarily a tree, this problem can be reformulated as a strictly convex quadratic programming problem. An application to symmetric bimatrix game is also presented.