The Minimum Mean Equitable Dominating Energy of Graphs

Abstract

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.