A topological index is a branch of chemical graph theory that is vital to analyzing the physio-chemical characteristics of chemical compound structures divided into a degree-based molecular structure such as Zagreb indices, a distance-based molecular structure such as Wiener index, and a mixed such as Gutman index. In this paper, some definitions, results, and examples of Wiener polynomial and index for subdivision graph of friendship, bifriendship graphs, line subdivision graph of friendship, and bifriendship graphs were introduced. Moreover, we used the MATLAB program to calculate the Wiener polynomial and index of these graphs and refer to some applications.

Mechanical Ventilation (MV) is a critical medical intervention used to support patients with impaired lung function caused by severe conditions such as pneumonia or COVID‐19. Model‐based Methods, particularly computational models, are employed to simulate and analyze lung mechanics under MV. Among these, the Single Compartment Lung Model (SCLM) remains the most commonly adopted framework for replicating lung behavior during MV, facilitating optimal treatment strategies. This review critically analyzes existing literatures on SCLM applications, focusing on key parameters such as lung elastance (E), airway resistance (R _rs ), and Dynamic Functional Residual Capacity (dFRC). Methodologies, evaluation metrics, and clinical applications were examined to identify common trends, inconsistences, and research gaps. The findings indicate that E has been the primary focus due to its relevance in assessing lung mechanism, especially under MV. This parameter often evaluated alongside variables like Positive End‐Expiratory Pressure (PEEP), Peak Inspiratory Pressure (PIP), Peak Inspiratory Volume (PIV), and Tidal Volume (V _t ). Additionally, FRC and R _rs are also considered in some models. The review emphasizes the need for standardized evaluation protocols, simplified input models, and disease‐specific adaptations to enhance clinical applicability. Our findings provide valuable guidance for future research aiming to refine SCLM‐based approaches and improve personalized mechanical ventilation strategies.