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For a simple graph G with vertex set V (G) and edge set E(G), let deg(u) be the degree of the vertex u ∈ V (G). The forgotten index of G and its coindex are defined as F (G) = ∑ v∈V (G) deg 3(v) and F (G) = ∑ uv 6∈E(G) [ deg2(u) + deg2(v) ] . New bonds for the first Zagreb indexM1(G) = ∑ v∈V (G) deg(v)2, forgotten index, and its coindex are obtained.

New Upper and Lower Bounds for Some Degree-based Graph Invariants