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The Harary index is defined as the sum of reciprocals of distances between all pairs of vertices of a connected graph. In this paper, the exact formulae for the Harary indices of tensor product G × Km0,m1,...,mr−1 and the strong product G⊠Km0,m1,...,mr−1 , where Km0,m1,...,mr−1 is the complete multipartite graph with partite sets of sizes m0,m1, . . . ,mr−1 are obtained. Also upper bounds for the Harary indices of tensor and strong products of graphs are estabilished. Finally, the exact formula for the Harary index of the wreath product G ○ G′ is obtained.

Spectrum‐based topological indices (eigenvalue‐based topological indices), a valuable tool for analyzing molecular structure. These topological indices are metrics that reflect the inherent characteristics of chemical substances, were employed in conjunction with quantitative structure‐property relationship (QSPR) to investigate nonsteroidal anti‐inflammatory drugs (NSAIDs) which are used toalleviate or eliminate pain sensations in affected areas. We have to use mathematica to compute various eigenvalue‐based indices and utilized statistical software to identify correlations between these indices and key physical properties of NSAIDs. The analysis revealed that specific indices, including EFZS$$ {E}_{FZS} $$ index, ρFZS$$ {\rho}_{FZS} $$ index, EISIS$$ {E}_{ISIS} $$ index, and EABCS$$ {E}_{ABCS} $$ index exhibited strong associations with properties like complexity and refractivity, boiling point, polarity, and molar weight, respectively. [ABSTRACT FROM AUTHOR]

In Sri Lanka as well as the rest of the globe, cancer is the top cause of mortality. One of the key medicines in treating tumors is anticancer medications and delivery dendrimers. To prevent the formation of the rapid proliferation of cancer cells, several tests were carried out. Because of this, research on dendrimers and anti-cancer medications is crucial. Topological indices (TIs) are molecular descriptors numerical values corresponding to the physical characteristics of a molecule's chemical structure. It costs money to determine a molecule's physical characteristics in a lab since it takes a lot of materials, medications, and time. Therefore, the relevant information about molecules may be obtained by computing TIs. This study's goals are to compute hitherto uncalculated eccentricity-based TIs for various anticancer structures and to use curvilinear regression models to forecast the physical characteristics of particular anticancer medications. These anticancer medications were given different TIs developed in this work, allowing the researchers to understand the physical, physicochemical, and chemical characteristics related to them. In addition comparative study of the novel indices with some well-known and mostly used indices in structure–property modeling and anticancer drugs in performed. [ABSTRACT FROM AUTHOR]

The threat of developing a cancer therapy has been there for the past two to three decades. Almost 10 million people worldwide are affected by this illness each year. Anticancer medications are those that are used to treat cancer, a malignant condition. These anticancer medications come in a variety of types, such as hormones, antimetabolites, and alkalizing agents. Numerous studies demonstrate a close relationship between the chemical structure of anticancer drugs and alkane characteristics including boiling, melting, and enthalpy. Some antiviral medications that are thought to hold promise for the treatment of cancer are examined in the planned research. For the chemical graphs of these medications, ST-polynomials based on status distance are computed. Numerous topological indices (TI) that depend on the status distance may be constructed by applying these polynomials. Additionally, the TIs are used in the creation of the QSPR models to estimate some of the physicochemical characteristics of these medications. Curve fitting is used to produce the QSPR research. [ABSTRACT FROM AUTHOR]

The reciprocal product degree distance RDD*(G), which is a weight version of the Harary index defined for a connected graph G as vertex-degree-weighted sum of the reciprocal distances, that is RDD*(G) = 1/2 Su,v∊V(G)dG(u)dG(v)/dG(u,v), where dG(u) denotes the degree of a vertex u in G and dG(u, v) denotes the distance between two vertices u and v in G. In this paper, we obtain an upper bound for reciprocal product degree distance of F-sum of graphs which is defined by Eliasi [4]. [ABSTRACT FROM AUTHOR]

The inverse connective eccentricity index of a connected graph G is defined as ..., where ϵG(u) and dG(u) are the eccentricity and degree of a vertex u in G, respectively. In this paper, we obtain an upper bounds for inverse connective eccentricity indices for various classes of graphs such as generalized hierarchical product graph and F-sum of graphs. [ABSTRACT FROM AUTHOR]