Phenol formaldehyde (phenolic resin) has a wide range of moldings. However, it immense consumption in manufacturing electrical equipment due to its insulating property. Phenolic resin retains properties at the freezing point, and also age cannot be determined. Due insulator property, use equipment. In this article, degree-based topological indices phenol are determined with help M-polynomial. W...

The concept of Zagreb eccentricity indices ( 1 E and 2 E ) was introduced in the chemical graph theory very recently. The eccentric connectivity index ( ) c ξ is a distance-based molecular structure descriptor that was used for mathematical modeling of biological activities of diverse nature. The second geometric-arithmetic index 2 ( ) GA was introduced in 2010, is found to be useful tool in QS...

Single-valued neutrosophic numbers (SVNNs) can express incomplete, indeterminate, and inconsistent information in the real world. Then, the common weighted aggregation operators of SVNNs may result in unreasonably aggregated results in some situations. Based on the hybrid weighted arithmetic and geometric aggregation and hybrid ordered weighted arithmetic and geometric aggregation ideas, this p...

Practical solid modeling systems are plagued by numerical problems that arise from using floating-point arithmetic. For example, polyhedral solids are often represented by a combination of geometric and combinatorial information. The geometric information may consist of explicit plane equations, with floatingpoint coefficients; the combinatorial information may consist of face, edge, and vertex...

There is a parallelism between growth in arithmetic combinatorics and growth in a geometric context. While, over R or C, geometric statements on growth often have geometric proofs, what little is known over finite fields rests on arithmetic proofs. We discuss strategies for geometric proofs of growth over finite fields, and show that growth can be defined and proven in an abstract projective pl...