Comparing Zagreb Indices of Cyclic Graphs

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On Zagreb indices of graphs (2023, background): “On the other hand, it is well known that M1(G) ≥ 4m(2) n (3)”
A Survey on Comparing Zagreb Indices (2011, background): “[12] Let G be a simple connected graph with ν independent cycles, n ≥ 5(ν − 1) vertices, m = n + ν − 1 edges, Zagreb indices M1 and M2 .”
On Vertex–Degree–Based Molecular Structure Descriptors (2011, background): “The Zagreb indices were first time considered in [21] and since then studied in hundreds of papers, see [22–24] and the references cited therein.”
Three New/Old Vertex-Degree-Based Topological Indices (2014, background): “this graph invariant is necessarily encountered within studies of the difference between the two Zagreb indices [3, 17, 32].”