Journal of Prime Research in Mathematics

Abstract: The Hosoya index counts the number of independent edge sets in a graph, that is the number of subsets of the edge set such that no two edges in the subset share a vertex. Moreover, the Hosoya index gives important details on a graph’s structural properties, including its connectivity. It has applications in a variety of fields, including computational biology, networking, and chemistry. In our article, we study Hosoya indiex of amalgamation of cycles and edge-amalgamation of cycles. Moreover, in this article we study the restricted Hosoya polynomial of amalgamation of cycles and we also give the general form of topological index.

Abstract: In this study, a multi-wing chaotic system with classical derivative has been studied. The conditions under which the existence and uniqueness of the solution of this chaotic system exist are examined. Afterwards, this chaotic system has been modified using fractional differential operators, and in this case the behavior of the multi-wing chaotic system has been investigated. Moreover, the newly introduced piecewise differential operators is included in such a chaotic system and the piecewise chaotic system is solved by using Newton polynomial approach. The numerical simulations of piecewise chaotic system are performed for fractional order.

Abstract: In this article, we consider the one-dimensional system of piezoelectric beams with thermal and magnetic effects in the presence of an infinite memory term acting on the mechanical equation. Under appropriate assumptions on the kernel, we prove that the system is well-posed in the sense of semigroup and by constructing a suitable Lyapunov functional. We establish that the system is exponentially stable. Moreover,our result does not depend on any relationship between system parameters.

Abstract: The study of networks by using topological indices (TIs) have been significantly become a useful attention in the physicochemical properties of compounds, pharmacology and drug delivery in the field of experimental sciences. Thus, TIs help us to study the new networks and they also play an essential role in the study of the quantitative structure property and activity relationships. In this paper, we compute the connection number (CN) based Zagreb indices in the form of first general-Zagreb connection index (ZCI), generalized first, second, third and fourth ZCIs of two rhombus type networks such as rhombus oxide and rhombus silicate. In particularly, we also find the first, second, modified first, second, third and fourth ZCIs by using main results of the abovementioned general & generalized connection based Zagreb indices. In addition, a comparison between degree and CN based Zagreb indices is done with the help of their numerical values and graphical demonstration

Abstract: Face irregularity strength under ρ−labeling ξ with class (α1, β1, γ1) of plane graphs is a labeling from the set of graph elements into the set of integers, that is, ξ: {V ∪ E ∪ F} → {1, 2, 3, .., ρ}, such that the face weights are distinct at any stage in the graph labeling, that is, Wξ(α1,β1,γ1)(f) ̸= Wξ(α1,β1,γ1)(g), for any two faces f and g of the graph G. The face irregular strength of a plane graph G is the least possible integer ρ such that G admits face irregular ρ−labeling. In this research, authors have examined the exact tight lower bounds for the face irregular strength of generalized plane graphs under ρ−labeling of class (α1, β1, γ1) for vertex (1, 0, 0), edge (0, 1, 0), face (0, 0, 1), vertex-face (1, 0, 1), edge-face (0, 1, 1) and entire (1, 1, 1). Results are verified by examples.

Abstract: This article introduces the concept of translation-factorable surfaces in the isotropic space 𝕀³ and presents classification theorems for these surfaces based on their isotropic mean and isotropic Gaussian curvatures, considering both zero and nonzero values. Furthermore, an additional investigation is conducted to classify translation-factorable (TF) surfaces in 𝕀³ under the condition H²=K