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