Note on properties of First Zagreb Index of Graphs

Let G be a graph. The first Zagreb M1(G) of graph G is defined as: M1(G) = uV(G) deg(u) 2. In this paper, we prove that each even number except 4 and 8 is a first Zagreb index of a caterpillar. Also, we show that the fist Zagreb index cannot be an odd number. Moreover, we obtain the fist Zagreb index of some graph operations