Mathematic

Chemical graph theory is a branch of mathematical chemistry which deals with the nontrivial applications of graph theory to solve molecular problems. A graph-based molecular descriptors commonly known as topological indices describe the structures of chemical compounds. They are used in the isomer discrimination, structure property relationship, structure activity relations. Also, the certain physicochemical properties such as boiling point, enthalpy of vaporization, stability, and so on are able to be predicted by this technique. Molecules and molecular compounds are often modeled by molecular graph which is a representation of the structural formula of a chemical compound in terms of graph theory. Recently, the Max-min rodeg index (Mm sde ) which is vertex degree-based topological index has attracted attention and gained popularity. This index give the best predictor for enthalpy of vaporization and standard enthalpy of vaporization in the set of octane isomers and also for log wa...

In the present work, we consider the fermionic p-adic q-integral of p-adic gamma function and the derivative of p-adic gamma function by using their Mahler expansions. The relationship between the p-adic gamma function and q-Changhee numbers is obtained. A new representation is given for the p-adic Euler constant. Also, we study on the relationship between qChanghee polynomials and p-adic Euler constant using the fermionic p-adic q-integral techniques the idea that the q-Changhee polynomial.

In the present work we consider the q-extension of the p-adic gamma function. We derive the Volkenborn integral of the q-extension of the p-adic gamma function by using its Mahler expansion. Moreover, we give a new representation for the q-extension of the p-adic Euler constant.

The p-adic gamma function is considered to obtain its derivative and to evaluate its the fermionic p-adic integral. Furthermore the relationship between the p-adic gamma function and Changhee polynomials and also between the Changhee polynomials and p-adic Euler constants is obtained. In addition, the p-adic Euler constants are expressed in term of Mahler coefficients of the p-adic gamma function.

The inverse sum indeg index \(ISI(G)\) of a graph is equal to the sum over all edges \(uv\in E(G)\) of weights \(\frac{d_{u}d_{v}}{d_{u}+d_{v}}\). This paper presents the relation between the inverse sum indeg index and the chromatic number. The bounds for the spectral radius of the inverse sum indeg matrix and the inverse sum indeg energy are obtained. Additionally, the Nordhaus-Gaddum-type results for the inverse sum indeg index, the inverse sum indeg energy and the spectral radius of the inverse sum index matrix are given.

Topological indices are the numerical descriptors of a molecular structure obtained via molecular graph G. They are used to predict physicochemical and bioactive properties of the molecules and molecular compounds. In this paper, the Mostar index is studied. It is presented the relationships between the Mostar index and other topological indices. Inequalities about some parameters and also Nordhaus-Gaddum-type results for the Mostar index are also presented.

Topological indices are the numerical descriptors of a molecular structure obtained via molecular graph G. Topological indices are used in the structure-property relationship, structure-activity relations, and nanotechnology. Also, they hold us to predict certain physicochemical properties such as boiling point, enthalpy of vaporization, stability, and so on. In this study, it is considered the Mostar index. It is present upper bound for Mostar index of bridge graphs. Moreover, it is given exact expressions for the Mostar index of bridge graphs of the path, star, cycle, and complete graphs.Publisher's Versio

The inverse sum indeg index \(ISI(G)\) of a graph is equal to the sum over all edges \(uv\in E(G)\) of weights \(\frac{d_{u}d_{v}}{d_{u}+d_{v}}\). In this paper, we calculated the inverse indeg indices and inverse indeg energies that give information about the physicochemical properties and biological characteristics of Hyaluronic Acid-Paclitaxel conjugates used in the production of drugs used in the treatment of cancer disease. This study presents the relation between the ISI index and the ISI energy of the molecular graph of Hyaluronic Acid-Paclitaxel conjugates.

Corona product of two fuzzy graphs which is analogous to the concept corona product operation in crisp graph theory is defined. The degree of an edge in corona product of fuzzy graphs is obtained. Also, the degree of an edge in fuzzy graph formed by this operation in terms of the degree of edges in the given fuzzy graphs in some particular cases is found. Moreover, it is proved that corona product of two fuzzy graphs is effective when two fuzzy graphs is effective fuzzy graphs.

Corona product of two fuzzy graphs which is analogous to the concept corona product operation in crisp graph theory is defined. The degree of an edge in corona product of fuzzy graphs is obtained. Also, the degree of an edge in fuzzy graph formed by this operation in terms of the degree of edges in the given fuzzy graphs in some particular cases is found. Moreover, it is proved that corona product of two fuzzy graphs is effective when two fuzzy graphs is effective fuzzy graphs.

In this study, the representation theorem and a partition for intuitionistic fuzzy sets were given. For those properties, intuitionistic fuzzy sheet t-level set, intuitionistic fuzzy α-t block level set and intuitionistic fuzzy t-subset were used.