Abstract
Given a graph G = (V, E), with respect to a vertex partition π« we associate a matrix called π«-matrix and define the π«-energy, Eπ« (G) as the sum of π«-eigenvalues of π«-matrix of G. Apart from studying some properties of π«-matrix, its eigenvalues and obtaining bounds of π«-energy, we explore the robust(shear) π«-energy which is the maximum(minimum) value of π«-energy for some families of graphs. Further, we derive explicit formulas for Eπ« (G) of few classes of graphs with different vertex partitions.