The Minimum Mean Equitable Dominating Energy of Graphs - M. V. Chakradhara Rao, B. Satyanarayana, K. A. Venkatesh (International Journal of Advanced Science and Technology, 2020)
The  sum of all absolute values of the Eigen values of  the adjacency matrix corresponding to G =(V,E) is the energy of a graph  .The covering energy of graph is first introduced by Adiga [1] and later the minimum equitable domination energy (MEDE) of G,  E_ED (G) is definedby Anita, A, Armugam S [6].Now we are interested about the minimum mean equitable domination energy (MMEDE), denoted by E_ED^M(G) of a graph G. The equitable dominating energy of G is the sum of all absolute values of the Eigen or characteristic values of its equitable dominating matrix. For any graph G of n vertices with M as its equitable dominating matrix, if e_1,e_2,...,e_n are the Eigen values of M and e ̅ is their average, then the equitable dominating energy[3,4] of graph is E_μ (G)= ∑_(i=1)^n▒| e_i|.The MMEDE of G is then descried [5] as E_μ^M(G) = ∑_(i=1)^n▒| e_i-e ̅|.We present the results on MMEDE of few standard graphs.