Abstract
The vertex-degree function index Hf(Γ) is defined as Hf(Γ)=∑v∈V(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¯).
Funder
the Qinghai Key Laboratory of Internet of Things Project
National Research Foundation funded by the Korean government
Subject
Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis
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