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Open AccessArticle

Maximizing and Minimizing Multiplicative Zagreb Indices of Graphs Subject to Given Number of Cut Edges

by Shaohui Wang 1,*,†, Chunxiang Wang 2,†, Lin Chen 2,†, Jia-Bao Liu 3,† and Zehui Shao 4,†
1
Department of Mathematics, Savannah State University, Savannah, GA 31419, USA
2
School of Mathematics and Statistics and Hubei key Laboratory Mathematics Sciences, Central China Normal University, Wuhan 430079, China
3
School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China
4
Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Mathematics 2018, 6(11), 227; https://doi.org/10.3390/math6110227
Received: 21 September 2018 / Revised: 19 October 2018 / Accepted: 22 October 2018 / Published: 29 October 2018
(This article belongs to the Special Issue Discrete Optimization: Theory, Algorithms, and Applications)
Given a (molecular) graph, the first multiplicative Zagreb index Π 1 is considered to be the product of squares of the degree of its vertices, while the second multiplicative Zagreb index Π 2 is expressed as the product of endvertex degree of each edge over all edges. We consider a set of graphs G n , k having n vertices and k cut edges, and explore the graphs subject to a number of cut edges. In addition, the maximum and minimum multiplicative Zagreb indices of graphs in G n , k are provided. We also provide these graphs with the largest and smallest Π 1 ( G ) and Π 2 ( G ) in G n , k . View Full-Text
Keywords: cut edge; graph transformation; multiplicative zagreb indices; extremal values cut edge; graph transformation; multiplicative zagreb indices; extremal values
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Wang, S.; Wang, C.; Chen, L.; Liu, J.-B.; Shao, Z. Maximizing and Minimizing Multiplicative Zagreb Indices of Graphs Subject to Given Number of Cut Edges. Mathematics 2018, 6, 227.

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