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Shannon entropy, also known as information entropy or entropy, measures the uncertainty or randomness of probability distribution. Entropy is measured in bits, quantifying the average amount of information required to identify an event from the distribution. Shannon's entropy theory initiates graph entropies and develops information-theoretic magnitudes for structural computational evidence of organic graphs and complex networks. Graph entropy measurements are valuable in several scientific fields, such as computing, chemistry, biology, and discrete mathematics. In this study, we investigate the entropy of fractal-type networks by considering cycle, complete, and star networks as base graphs using degree-based topological indices. [ABSTRACT FROM AUTHOR]

The molecular graph theory is one of the essential tools for developing and constructing molecular structure. In particular, using topological invariant, which is a numerical descriptor of molecular graph, has become widespread in predicting physical properties. Topological indices provide knowledge about the overall form of molecular graphs, particularly various degree-based topological indices. This research paper focuses on the first and second Zagreb index and their coindices for the line graph of a transition metal-organic network. The network, denoted by L (TM − TCNB) , comprises the transition metals Ti, V, Cr, Fe, Co, Ni, Cu or Zn, and the TCNB ligand. The line graph of a network is a graph that represents the connections between the edges of the original network. The Zagreb indices are widely used to describe the molecular graph's shape and structure. The paper highlights the importance of these indices in modelling the chemical properties of the transition metal-organic network. The study results show that the Zagreb indices and their coindices strongly correlate with several physical characteristics, for instance the boiling points, melting points, and density of the network. [ABSTRACT FROM AUTHOR]

L-valine is considered one of the essential amino acids for mammals, which belongs to the glycogen types of amino acids. This amino acid is valuable for making protein. Due to the diverse structure of N-salicylidene-L-valine and its higher catalytic and cytotoxic activity it gains impressive interest. To study this structure more deeply and to know more about its properties in terms of topological indices, we study the supramolecular chain in dialkyltin of complex- 2 , 3 , and 4 of N-salicylidene-L-valine. In the end, we provide a comparative study of these structures by taking particular examples and also gives a comparison between topological indices. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the degree based topological properties of the novel planar metal-organic networks TM – TCNB. Interestingly, the TM – TCNB systems are metallic in any event in one turn heading and show long-run ferromagnetic coupling on the off chance that for attractive structures, which speak to perfect applicants and a fascinating possibility of uncommon applications in spintronics. Chemical graph theory plays an important role in modeling and designing any chemical structure. The topological indices are the numerical invariants of a molecular graph and are very useful for predicting their physical properties. We have computed the degree based topological indices for this metal-organic networks TM – TCNB. [ABSTRACT FROM AUTHOR]

Topological indices are empirical features of graphs that characterize the topology of the graph and, for the most part, are graph independent. An important branch of graph theory is chemical graph theory. In chemical graph theory, the atoms corresponds vertices and edges corresponds covalent bonds. A topological index is a numeric number that represents the topology of underline structure. In this article, we examined the topological properties of prism octahedron network of dimension m and computed the total eccentricity, average eccentricity, Zagreb eccentricity, geometric arithmetic eccentricity, and atom bond connectivity eccentricity indices, which are used to utilize the distance between the vertices of a prism octahedron network. [ABSTRACT FROM AUTHOR]

A branch of graph theory that makes use of a molecular graph is called chemical graph theory. Chemical graph theory is used to depict a chemical molecule. A graph is connected if there is an edge between every pair of vertices. A topological index is a numerical value related to the chemical structure that claims to show a relationship between chemical structure and various physicochemical attributes, chemical reactivity, or, you could say, biological activity. In this article, we examined the topological properties of a planar octahedron network of m dimensions and computed the total eccentricity, average eccentricity, Zagreb eccentricity, geometric arithmetic eccentricity, and atom bond connectivity eccentricity indices, which are used to determine the distance between the vertices of a planar octahedron network. [ABSTRACT FROM AUTHOR]