Note on two generalizations of the Randić index

Shi, Yongtang

doi:10.1016/j.amc.2015.06.019

Cited by 69 publications

(32 citation statements)

References 21 publications

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“…In the future we would like to explore some properties of the above spectrum-based indices and also some other topological indices (such as Randić index [39][40][41][42][43][44][45], Wiener index [46][47][48][49][50][51] and graph entropies [52][53][54]) of mixed graphs.…”

Section: Resultsmentioning

confidence: 99%

Hermitian Laplacian matrix and positive of mixed graphs

2015

Applied Mathematics and Computation

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Section: Resultsmentioning

confidence: 99%

Hermitian Laplacian matrix and positive of mixed graphs

2015

Applied Mathematics and Computation

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“…Many results of the applications on Zagreb indices were explored in [5]. Recently, there are hundreds of articles investigated Zagreb indices in the area of chemistry and mathematics [6,7,8,9,10,11,12].…”

Section: Introductionmentioning

confidence: 99%

On extremal multiplicative Zagreb indices of trees with given domination number

Wang

Liu

2018

Applied Mathematics and Computation

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For a graph G, the first multiplicative Zagreb index 1 is equal to the product of squares of the vertex degrees, and the second multiplicative Zagreb index 2 is equal to the product of the products of degrees of pairs of adjacent vertices. The (mutiplicative) Zagreb indices have been the focus of considerable research in computational chemistry dating back to Gutman and Trinajstić in 1972. In this paper, we explore the mutiplicative Zagreb indices in terms of arbitrary domination number. The sharp upper and lower bounds of 1 (G) and 2 (G) are given. In addition, the corresponding extreme graphs are charaterized.By the recursive process, we see thatRecently, multiplicative Zagreb indices attracted extensive attention in physics, chemistry, graph theory, etc. Xu and Hua [18] proposed a unified approach to characterize extremal (maximal and minimal) trees, unicyclic graphs and bicyclic graphs with respect to multiplicative Zagreb indices, respectively. Iranmanesh et al. [19] investigated these indices the first and the second multiplicative Zagreb indices for a class of dendrimers. Liu and Zhang [14] introduced several sharp upper bounds for π 1 -index and π 2 -index in terms of graph parameters including the order, size and radius [20]. Wang and Wei [21] studied these indices in k-trees and extremal k-trees were characterized. Ramin Kazemi [24] obtained the bounds for the moments and the probability generating function of these indices in a randomly chosen molecular graph with tree structure of order n. Bojana Borovićanin et al. [25] presented upper bounds on Zagreb indices of trees in terms of domination number. Also, a lower bound for the first Zagreb index of trees with a given domination number is determined and the extremal trees are characterized as well. Motivated by the above results, in this paper we further investigate the multiplicative Zagreb indices of trees in terms of domination number. This enriches and extends some earlier results obtained by Bojana Borovićanin et al. [25].

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“…Mathematicians have exhibited considerable interest in the properties of Zagreb indices about the extremal values or bounds for the topological indices of graphs, as well as related problems of characterizing the extremal graphs [9,10,11,12,13,14,15,16,17,18,19]. In addition to a plenty of * Authors' email addresses: S. Wang (shaohuiwang@yahoo.com), C. Wang (wcxiang@mail.ccnu.edu.cn), L. Chen (409137414@qq.com).…”

Section: Introductionmentioning

confidence: 99%

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

Wang

Chen

et al. 2018

Mathematics

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For a molecular graph, the first multiplicative Zagreb index Π 1 is equal to the product of the square of the degree of the vertices, while the second multiplicative Zagreb index Π 2 is equal to the product of the endvertex degree of each edge over all edges. Denote by G n,k the set of graphs with n vertices and k cut edges. In this paper, we explore graphs in terms of a number of cut edges. In addition, the maximum and minimum multiplicative Zagreb indices of graphs with given number of cut edges are provided. Furthermore, we characterize graphs with the largest and smallest Π 1 (G) and Π 2 (G) in G n,k , and our results extend and enrich some known conclusions.

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Note on two generalizations of the Randić index

Cited by 69 publications

References 21 publications

Hermitian Laplacian matrix and positive of mixed graphs

Hermitian Laplacian matrix and positive of mixed graphs

On extremal multiplicative Zagreb indices of trees with given domination number

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

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