Inequalities involving the harmonic-arithmetic index.

Autor: Ali, Akbar, Milovanović, Emina, Stankov, Stefan, Matejić, Marjan, Milovanović, Igor
Zdroj: Afrika Matematica; Jun2024, Vol. 35 Issue 2, p1-10, 10p
Abstrakt: Let G be a simple graph with vertex set V = { v 1 , v 2 , … , v n } . The notion i ∼ j is used to indicate that the vertices v i and v j of G are adjacent. For a vertex v i ∈ V , let d i be the degree of v i . The harmonic-arithmetic (HA) index of G is defined as H A (G) = ∑ i ∼ j 4 d i d j (d i + d j) - 2 . In this paper, a considerable number of inequalities involving the HA index and other topological indices are derived. For every obtained inequality, all the graphs that satisfy the equality case are also characterized. [ABSTRACT FROM AUTHOR]
Databáze: Complementary Index
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