A note on the first reformulated Zagreb index

Let G=(V,E),G=(V,E),V={1,2,…,n},V={1,2,…,n},E={e1,e2,…,em},E={e1,e2,…,em}, be a simple graph with n vertices and m edges. Denote by d(ei  ) (i=1,2,…,mi=1,2,…,m) an edge degree, and by EM1=∑i=1md(ei)2 first reformulated Zagreb index of graph G. Upper and lower bounds of graph invariant EM1 are obtained.