Abstract
Abstract Energy of a molecule plays an important role in physics, chemistry and biology. In mathematics, the concept of energy is used in graph theory to help other subjects such as chemistry and physics. In graph theory, nullity is the number of zeros extracted from the characteristic polynomials obtained from the adjacency matrix, and inertia represents the positive and negative eigenvalues of the adjacency matrix. Energy is the sum of the absolute eigenvalues of its adjacency matrix. In this study, the inertia, nullity and signature of the aforementioned structures have been discussed.
Highlights
A molecular graph is a mathematical object defined as G = (V, E), where V is the set of vertices called atoms and E is the set of edges called bonds
The eigenvalues play an important role in the field of mathematics, but these values are very important in other fields such as chemistry, economics and many more
As far as our study concerns about eigenvalues, these values interpret in chemistry as the form of energy and as different physicochemical properties of a chemical compound
Summary
A molecular graph is a mathematical object defined as G = (V, E), where V is the set of vertices called atoms and E is the set of edges called bonds. The eigenvalues play an important role in the field of mathematics, but these values are very important in other fields such as chemistry, economics and many more. As far as our study concerns about eigenvalues, these values interpret in chemistry as the form of energy and as different physicochemical properties of a chemical compound. The signature s(G) of the graph G is just a number that is generated by the difference in the number of positive and negative eigenvalues. It is observed that phenylene and anthracene are stable, closed-shell molecules because they are represented by their nullity which is equal to zero
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