engleski

Comparing the Zagreb Indices

Let G = (V, E) be a simple graph with n = vertical bar V vertical bar vertices and m = vertical bar E vertical bar edges ; let d(1), d(2), ..., d(n) denote the degrees of the vertices of G. If Delta = max d(i) <= 4, G is a chemical graph. The first and second Zagreb indices are defined as [GRAPHICS] We show that for all chemical graphs M-1/n <= M-2/m. This does not hold for all general graphs, connected or not.

Zagreb indices; extremal graph theory; inequalities

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