The total version of geometric–arithmetic index of graphs is introduced based on the endvertex degrees of edges of their total graphs. In this paper, beside of computing the total GA index for some graphs, its some properties especially lower and upper bounds are obtained.

The vertex-degree function index Hf(Γ) is defined as Hf(Γ)=∑v∈V(Γ)f(d(v)) for a f(x) on non-negative real numbers. In this paper, we determine the extremal graphs with maximum (minimum) vertex degree in set of all n-vertex chemical trees, and connected graphs. We also present Nordhaus–Gaddum-type results Hf(Γ)+Hf(Γ¯) Hf(Γ)·Hf(Γ¯).

Recent empirical evaluations of exact algorithms for Feedback Vertex Set have demonstrated the efficiency a highest-degree branching algorithm with degree-based pruning. In this paper, we prove that empirically fast runs in $$O(3.460^k n)$$ time, where k is solution size. This improves previous best $$O(3.619^k -time deterministic obtained by Kociumaka and Pilipczuk (Inf Process Lett 114:556–56...

A topological index can be focused on uprising of a chemical structure into real number. The degree-based indices have an active place among all indices. These descriptors intentionally associate certain physicochemical assets the corresponding compounds. Graph theory plays very useful role in such type research directions. hex-derived networks vast applications computer science, physical scien...