The first and second Zagreb indices of some graph operations

By M. H. Khalifeh, H. Yousefi-Azari, Ali Reza Ashrafi. Discrete Applied Mathematics, 2009

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On leap Zagreb indices of graphs (2017, background): “[18] Let G1 and G2 be connected graphs with ni = |V (Gi)|, mi = |E(Gi)|, i = 1, 2.”
On the eccentric distance sum of graphs (2011, unknown): “In [11,18,25,34], the authors obtained the eccentric connectivity index, the first and second Zagreb index, the PI index and the Wiener-type indices of some graph operations.”
On Comparing Zagreb Indices of Graphs (2012, unknown): “[17] Let G1, G2, .”
The third and hyper-Zagreb coindices of some graph operations (2016, background): “For the proof of (c-e) were refer to [12,13].”
On the harmonic index of graph operations (2015, background): “In this paper, expressions for the Harmonic indices of the join, corona product, Cartesian product, composition and symmetric difference of graphs are derived[1],[3],[10],[13],[15],[9].”