Abstract
Zagreb indices and their modified versions of a molecular graph are important molecular descriptors which can be applied in characterizing the structural properties of organic compounds from different aspects. In this article, by exploring the structures of the quasi-tree graphs with given different parameters (order, perfect matching and number of pendant vertices) and using the properties of the general multiplicative Zagreb indices, we determine the minimal and maximal values of general multiplicative Zagreb indices on quasi-tree graphs with given order, with perfect matchings, and with given number of pendant vertices. Furthermore, we present the minimal and maximal values of general multiplicative Zagreb indices on trees with perfect matchings.
Highlights
Topological molecular descriptors are mathematical invariants reflecting some biological and physico-chemical properties of organic compounds on the chemical graph, and they play a substantial role in materials science, chemistry and pharmacology, etc
The famous Zagreb indices is one of the first topological molecular descriptors. They are first introduced by Gutman and Trinajstić [8] and used to examine the structure dependence of total π -electron energy on molecular orbital
GENERAL MULTIPLICATIVE ZAGREB INDICES OF TREES WITH A PERFECT MATCHING Let T 2m be the tree of order 2m arisen from Sm+1 by adding one pendant edge to its m − 1 pendant vertices
Summary
Topological molecular descriptors are mathematical invariants reflecting some biological and physico-chemical properties of organic compounds on the chemical graph, and they play a substantial role in materials science, chemistry and pharmacology, etc. (see [6], [7], [15]). Vetrík and Balachandran [18] determined the minimal and maximal general multiplicative Zagreb indices for trees with fixed order or segments or branching vertices or number of pendant vertices, and they identified the extremal trees. Sun: Quasi-Tree Graphs With Extremal General Multiplicative Zagreb Indices to detect the chemical compounds which may have desirable properties. If one can find some properties well-correlated with these two descriptors for some value of α, the extremal graphs should correspond to compounds with minimum or maximum value of that property One such property has already been found for multiplicative Zagreb indices. Since general multiplicative Zagreb indices for some value of α can correlate with biological, physico-chemical and other properties of chemical compounds, we use graph theory to characterize these chemical structures. The minimal and maximal values of general multiplicative Zagreb indices on trees with perfect matchings are presented
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