Opuscula Math. 39, no. 3 (2019), 433-446
https://doi.org/10.7494/OpMath.2019.39.3.433
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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- Tomáš Vetrík
https://orcid.org/0000-0002-0387-7276- University of the Free State, Department of Mathematics and Applied Mathematics, P.O. Box 339, 9300 Bloemfontein, South Africa
- Selvaraj Balachandran
- 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.
