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

Shaohui Wang, Chunxiang Wang, Lin Chen, Jia-Bao Liu and Zehui Shao
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Shaohui Wang: Department of Mathematics, Savannah State University, Savannah, GA 31419, USA
Chunxiang Wang: School of Mathematics and Statistics and Hubei key Laboratory Mathematics Sciences, Central China Normal University, Wuhan 430079, China
Lin Chen: School of Mathematics and Statistics and Hubei key Laboratory Mathematics Sciences, Central China Normal University, Wuhan 430079, China
Jia-Bao Liu: School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China
Zehui Shao: Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China

Mathematics, 2018, vol. 6, issue 11, 1-10

Abstract: 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 .

Keywords: cut edge; graph transformation; multiplicative zagreb indices; extremal values (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
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