Multiplicative Versions of First Zagreb Index

  title={Multiplicative Versions of First Zagreb Index},
  author={Mehdi Eliasi and Ali Iran and anesh and I. T. Gut},
The first Zagreb index of a graph G, with vertex set V (G) and edge set E(G), is defined as M1(G) = ∑ u∈V (G) d(u) 2 where d(u) denotes the degree of the vertex v. An alternative expression for M1(G) is ∑ uv∈E(G)[d(u) + d(v)]. We consider a multiplicative version of M1 defined as Π∗1(G) = ∏ uv∈E(G)[d(u) + d(v)]. We prove that among all connected graphs with a given number of vertices, the path has minimal Π∗1. We also determine the trees with the second–minimal Π∗1. 
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Simple topological index

  • H. Narumi, M. Katayama
  • A newly devised index characterizing the…
  • 1984
Highly Influential
3 Excerpts


  • I. Gutman
  • Furtula (Eds.), Distance in Molecular Graphs…
  • 2012
1 Excerpt

So m e properties of the Naru m i – Kataya m a index

  • B. Ruščić I. Gut m an, N. Trinajstić, C. F. Wilcox
  • Appl . Math . Lett . , sub m itted
  • 2012

On vertex– degree–based molecular structure descriptors

  • T. Došlić, B. Furtula, A. Graovac, I. Gutman, S. Moradi, Z. Yarahmadi
  • MATCH Commun. Math. Comput. Chem. 66
  • 2011
2 Excerpts

Yarah m adi , On vertex – degree – based m olecular structure descriptors

  • B. Furtula T. Došlić, A. Graovac, Z.
  • MATCH Commun . Math . Comput . Chem .
  • 2011

Nanomolecules and Nanostructures – Polynomials and Indices

  • M. V. Diudea
  • Univ. Kragujevac, Kragujevac
  • 2010
1 Excerpt

On Zagreb indices

  • N. Trinajstić, S. Nikolić, A. Miličević, I. Gutman
  • Kem. Ind. 59
  • 2010
1 Excerpt

Molecular Descriptors for Chemoinformatics

  • R. Todeschini, V. Consonni
  • Wiley– VCH, Weinheim
  • 2009
1 Excerpt

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