Abstract
In this work, by using the properties of the variable sum exdeg indices and analyzing the structure of the quasi-tree graphs and unicyclic graphs, the minimum and maximum variable sum exdeg indices of quasi-tree graphs and quasi-tree graphs with perfect matchings were presented; the minimum and maximum variable sum exdeg indices of unicyclic graphs with given pendant vertices and cycle length were determined.
Highlights
Topological indices are mathematical descriptors reflecting some structural characteristics of organic molecules on molecular graphs, and they play an important role in pharmacology, chemistry, etc. ([1,2,3])
Where a ∈ (0, 1) ∪ (1, +∞) and dG(v) is the degree of vertex v. is graph invariant has a good correlation with the octanol-water partition coefficient [4] and was used to study the octane isomers given by the International Academy of Mathematical Chemistry (IAMC) [5,6,7]
Erefore, our results may be used to predict the extremal properties of organic molecules
Summary
Where a ∈ (0, 1) ∪ (1, +∞) and dG(v) is the degree of vertex v. is graph invariant has a good correlation with the octanol-water partition coefficient [4] and was used to study the octane isomers given by the International Academy of Mathematical Chemistry (IAMC) [5,6,7]. By using the technique of majorization, Ghalavand and Ashrafi [9] provided the maximal and minimal SEIa (for a > 1) of trees, bicyclic graphs, unicyclic graphs, and tricyclic graphs. We use NG(v) to denote the neighbourhood of a vertex v and ni to denote the number of vertices with degree i.
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