The purpose of this paper is to introduce and investigate the symmetric division deg energy SDDE(G) of a graph. We establish upper and lower bounds for SDDE (G). Also the symmetric division deg energy for certain graphs with one edge deleted are calculated.

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Motivated by the inverse sum status index, we introduce the inverse sum status matrix ISS={■((σ_u σ_v)/((σ_u+σ_v ) ) if u_i~v_j,@0 otherwise)┤ Thus we also obtained the results for well known graphs. Keywords: Inverse sum status energy, Inverse Sum Indeg matrix. 2010 AMS Subject Classification: 05C50.

The partition energy of a graph was introduced by Sampathkumar et al. [12]. Motivated by this, we introduce the concept of minimum equitable dominating partition energy of a graph, E E p (G) and compute the minimum equitable dominating partition energy E E p (G) of few families of graphs. Also, we establish the bounds for minimum equitable dominating partition energy.