The first Leap Zagreb coindex of some graph operations

In the last years, Naji et al. have introduced leap Zagreb indices conceived depending on the second degrees of vertices, where the second degree of a vertex $v$ in a graph $G$ is equal to the number of its second neighbors and denoted by $d_2(v/G)$.  Analogously, the leap Zagreb coindices were introduced by Ferdose and Shivashankara. The first leap Zagreb coindex of a graph is defined as  $\overline{L_1}(G)=\sum_{uv\not\in E_2(G)}(d_2(u)+d_2(v))$, where $E_2(G)$ is the 2-distance (second) edge set of $G$, In this paper, we present explicit exact expressions for the first leap Zagreb coindex $\overline{L_1}(G)$ of some graph operations.