On the edge-version atom-bond connectivity and geometric arithmetic indices of certain graph operations

Wei

2019

Filomat

Self Cite

For a (molecular) graph, the first multiplicative Zagreb index 1 (G) is the product of the square of every vertex degree, and the second multiplicative Zagreb index 2 (G) is the product of the products of degrees of pairs of adjacent vertices. In this paper, we explore graphs in terms of (edge) connectivity. The maximum and minimum values of 1 (G) and 2 (G) of graphs with connectivity at most k are provided. In addition, the corresponding extremal graphs are characterized, and our results extend and enrich some known conclusions.

Section: Introductionmentioning

confidence: 99%

Sharp bounds for the modified multiplicative Zagreb indices of graphs with vertex connectivity at most k

Wei

2019

Filomat

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“…Zagreb indices are employing as molecular descriptors in QSPR and QSAR, see [11,12]. In the interdisplinary of mathemactics, chemistry and physics, it is not surprising that there are numerous studies of properties of the Zagreb indices of molecular graphs [13,14,15,16,17,18,19,20,21]. In [22,23], some bounds of (chemical) trees on Zagreb indices are studied and surveyed.…”

Section: Introductionmentioning

confidence: 99%

On the sharp lower bounds of Zagreb indices of graphs with given number of cut vertices

Journal of Mathematical Analysis and Applications

2018

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The first Zagreb index of a graph G is the sum of the square of every vertex degree, while the second Zagreb index is the sum of the product of vertex degrees of each edge over all edges. In our work, we solve an open question about Zagreb indices of graphs with given number of cut vertices. The sharp lower bounds are obtained for these indices of graphs in V n,k , where V n,k denotes the set of all n-vertex graphs with k cut vertices and at least one cycle. As consequences, those graphs with the smallest Zagreb indices are characterized.

“…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

Chen

et al. 2018

Mathematics

Self Cite

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.