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The weight of an edge uv of a graph is defined to be the sum of degrees of the vertices u and v. The weight of a non-empty graph G is the minimum of the weights of edges of G. The paper is concerned with the maximum weight of a planar graph having n vertices and m edges. It is shown that if m≥2n+1, then the maximum weight is at most ⌊9m−12nm−2n⌋. Moreover, there are infinitely many pairs (n,m) such...
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