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 d 2 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 .

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