Bounds on the energy of a graph and its relation with topological indices

On Topological Indices and Arithmetic–Geometric Energy of Graphs

Let Γ be a graph of order n with m edges, and let Aag(Γ) denote its arithmetic–geometric matrix. The eigenvalues of Aag(Γ) are referred to as the arithmetic–geometric eigenvalues of Γ. The sum of the absolute values of these eigenvalues is called the arithmetic–geometric energy of Γ. In this paper, we establish some ne...

On Bounds for the Energy and Arithmetic Geometric Radius of Ape´ry Poset Graphs

.The energy and arithmetic-geometric radius are two important indices used to measure the network complexity, molecular properties, connectivity and stability of graphs. In this article, several parameters of Ape´ry poset graphs have been computed. Moreover, based on these graph parameters, some sharp bounds for the en...

Sharp Bounds for Kulli-Basava Indices of Graphs

In this paper, we establish formulas and sharp bounds for general Kulli-Basava indices and characterize graphs that attain these bounds. These indices have been shown to possess strong discriminating power for distinguishing nonisomorphic chemical structures. They are based on the edge neighborhood degrees of vertices...

Theory & Applications of Graphs Theory

A Remark on the Energy Bounds and Degree-Based Topological Indices of the Zero-Divisor Graph ℤₚ[x]/⟨x⁴⟩

The zero-divisor graph of a commutative ring, Γ(R), is a prominent subject in graph theory. Previous research has investigated the energy and topological indices of Γ(ℤₚ[x]/⟨x⁴⟩) for any prime p; however, errors were identified in the characteristic polynomial and the associated energy bounds. Recent work by Rather add...

ON TOPOLOGIES INDUCED BY HOP NEIGHBORHOODS OF GRAPHS

In this paper, we investigate structural properties of simple connected undirected graphs through a topology on the vertex set induced by their hop neighborhoods. In this construction, we characterize the classes of graphs that induce the discrete and indiscrete topologies. We also characterize the singleton sets in th...