Opuscula Math. 39, no. 3 (2019), 433-446

Opuscula Mathematica

General multiplicative Zagreb indices of graphs with given clique number

Tomáš Vetrík
Selvaraj Balachandran

Abstract. We obtain lower and upper bounds on general multiplicative Zagreb indices for graphs of given clique number and order. Bounds on the basic multiplicative Zagreb indices and on the multiplicative sum Zagreb index follow from our results. We also determine graphs with the smallest and the largest indices.

Keywords: clique number, multiplicative Zagreb index, chromatic number.

Mathematics Subject Classification: 05C35, 05C07.

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  • Selvaraj Balachandran
  • ORCID iD https://orcid.org/0000-0003-2782-6315
  • University of the Free State, Department of Mathematics and Applied Mathematics, P.O. Box 339, 9300 Bloemfontein, South Africa
  • SASTRA Deemed University, Department of Mathematics, School of Humanities and Sciences, 613402 Thanjavur, Tamil Nadu, India
  • Communicated by Mirko Horňák.
  • Received: 2018-08-17.
  • Accepted: 2018-11-21.
  • Published online: 2019-02-23.
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Cite this article as:
Tomáš Vetrík, Selvaraj Balachandran, General multiplicative Zagreb indices of graphs with given clique number, Opuscula Math. 39, no. 3 (2019), 433-446, https://doi.org/10.7494/OpMath.2019.39.3.433

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