Multiplicative Zagreb indices of k-trees

Abstract

Let G be a graph with vetex set V (G) and edge set E(G). The first generalizedfor a real number c > 0, and the second multiplicative Zagreb index is 2are the degrees of the vertices of u, v. The multiplicative Zagreb indices have been the focus of considerable research in computational chemistry dating back to Narumi and Katayama in 1980s. In this paper, we generalize Narumi-Katayama index and the first multicative index, where c = 1, 2, respectively, and extend the results of Gutman to the generilized tree, the k-tree, where the results of Gutman are for k = 1. Additionally, we characterize the extremal graphs and determine the exact bounds of these indices of k-trees, which attain the lower and upper bounds.

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

“…Xu and Hua [28] provided a unified approach to extremal multiplicative Zagreb indices for trees, unicyclic and bicyclic graphs. Sharp upper and lower bounds of these indices about k-trees are introduced by Wang and Wei [29]. Liu and Zhang provided several sharp upper bounds for multiplicative Zagreb indices in terms of graph parameters such as the order, size and radius [30].…”

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

“…One type of the most classical topological molecular descriptors is named as Zagreb indices M 1 and M 2 [2], which are literal quantities in an expected formula for the total π-electron energy of conjugated molecules. In the view of successful considerations on the applications on Zagreb indices [3], [4,5,6] introduced the multiplicative variants of molecular structure descriptors, denoted by Π 1 and Π 2 the multiplicative Zagreb indices. (Multiplicative) Zagreb indices are employed as molecular descriptors in QSPR and QSAR, see [7,8].…”

“…Borovićanin et al [21] investigated upper bounds on Zagreb indices of trees in terms of domination number and extremal trees are characterized. Wang and Wei [6] introduced sharp upper and lower bounds of these indices in k-trees. Liu and Zhang [14] provided several sharp upper bounds for π 1 -index and π 2 -index in terms of graph parameters such as the order, size and radius [27].…”

Note on the multiplicative Zagreb indices

“…Xu and Hua [20] obtained a unified approach to characterize extremal (maximal and minimal) trees, unicyclic graphs and bicyclic graphs with respect to multiplicative Zagreb indices, respectively. Recently, Wang and Wei studied these indices in k-trees [19].…”