engleski

Some Observations on Comparing Zagreb Indices

Let G be a simple graph possessing n vertices and m edges. Let di be the degree of the i-th vertex of G , i = 1, . . . , n . The first Zagreb index M1 is the sum of d2 i over all vertices of G. The second Zagreb index M2 is the sum di dj over pairs of adjacent vertices of G. In this paper we search for graph for which M1/n = M2/m, and show how numerous such graphs can be constructed. In addition, we find examples of graphs for which M1/n > M2/m, which are counterexamples for the earlier conjectured inequality M1/n ≤ M2/m.

Zagreb indices; inequality

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