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13 pages, 305 KB  
Article
Extremal Graphs to Vertex Degree Function Index for Convex Functions
by Dong He, Zhen Ji, Chenxu Yang and Kinkar Chandra Das
Axioms 2023, 12(1), 31; https://doi.org/10.3390/axioms12010031 - 27 Dec 2022
Cited by 8 | Viewed by 2130
Abstract
The vertex-degree function index Hf(Γ) is defined as Hf(Γ)=vV(Γ)f(d(v)) for a function f(x) defined on non-negative [...] Read more.
The vertex-degree function index Hf(Γ) is defined as Hf(Γ)=vV(Γ)f(d(v)) for a function f(x) defined on non-negative real numbers. In this paper, we determine the extremal graphs with the maximum (minimum) vertex degree function index in the set of all n-vertex chemical trees, trees, and connected graphs. We also present the Nordhaus–Gaddum-type results for Hf(Γ)+Hf(Γ¯) and Hf(Γ)·Hf(Γ¯). Full article
(This article belongs to the Special Issue Spectral Graph Theory, Molecular Graph Theory and Their Applications)
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