Comparing the Zagreb Indices
By Pierre Hansen, Damir Vukicevic. 2007
104 citations recorded by the source corpus.
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.
View Paper: https://www.semanticscholar.org/paper/cf5aaf4c042614eeeef754b58f323a88dd991c61
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Citations in the corpus
- On the multiplicative Zagreb coindex of graphs (2013, background): “The main properties of M1 and M2 were summarized in [6,7,11,17–19].”
- A Survey on Comparing Zagreb Indices (2011, background): “Stevanović [15] gave counter-examples to Conjecture 1.”