Variable Zagreb Indices and Karamata’s Inequality
نویسندگان
چکیده
For a simple graph G with n vertices and m edges, the inequality M1(G)/n ≤ M2(G)/m, where M1(G) and M2(G) are the first and the second Zagreb indices of G, is known as Zagreb indices inequality. Generalization of these indices gives first M1(G) and second M2(G) variable Zagreb indices. Vukičević in [13] has given an incomplete proof for the claim: for all simple graphs and all λ ∈ [0, 12 ], holds M1(G)/n ≤ M2(G)/m. Here we present a complete proof using Karamata’s inequality.
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