Doubly resolving sets (DRSs) provide a promising approach for source detection. They consist of minimal subsets of nodes with the smallest cardinality, referred to as the double metric dimension (DMD), that can uniquely identify the location of any other node within the network. Utilizing DRSs can improve the accuracy and efficiency of the identification of the origin of a diffusion process. This ability is crucial for early intervention and control in scenarios such as epidemic outbreaks, misinformation spreading in social media, and fault detection in communication networks. In this study, we computed the DMD of flower snarks $J_m$ and quasi-flower snarks $G_m$ by describing their minimal doubly resolving sets (MDRSs). We deduce that the DMD for the flower snarks $J_m$ is finite and depends on the network's order, and the DMD for the quasi-flower snarks $G_m$ is finite and independent of the network's order. Furthermore, our findings offer valuable insights into the structural features of complex networks. This knowledge can offer direction for future studies in network theory and its practical implementations.

Academics encounter a challenge regulating data-driven unpredictability in numerous complicated decision scenarios. Regulating the cyclical nature of appraisal attributes, determining lower and higher limitations, granting multi-parametric values as a means of assessing argumentation, and modeling uncertainty are a few examples of these problems. It requires the incorporation of complex plane settings, interval-valued intuitionistic fuzzy settings, and hypersoft settings. Inspired by these kinds of scenarios, the goal of this research was to articulate a new theoretical framework, the interval-valued complex intuitionistic fuzzy hypersoft set ( $\mathrm{\Gamma }$-set), which can handle these kinds of problems as a whole under the umbrella of a single framework. First, the concepts of $\mathrm{\Gamma }$-set, as well as its set operations and aggregations, such as decision matrix, cardinal matrix, aggregate matrix, and cardinality set, were examined. The second phase offers an appealing algorithm that consists of nine steps that go from taking into account necessary set construction to making the best choice. A prototype case study analyzing eighteen evaluation qualities and thirty-four sub-attributes for determining an optimal cooling system ( $\mathbb{C}\mathbb{S}\mathbb{Y}\mathbb{S})$ for a factory validates the provided algorithm. Informative comparison analysis and preferred study features were provided as essential components of research to assist academics in making significant advances regarding their field and gradually, but thoroughly, advancing their specialization.

The focus of this article lies on the notion of the edge version of doubly resolving sets (EVDRSs) in circulant networks. EVDRSs refer to unique edge subsets that are necessary for identifying individual edges in a network and distinguishing them based on their edge distances to the elements of the EVDRS. The main objectives were to define the minimal size of EVDRSs for circulant networks $C_n(1,2)$ and to investigate their basic properties. The systematic research helped to achieve a new understanding of the existence, construction, and characterization of EVDRSs in circulant networks $C_n(1,2)$. It is established that the EVDRSs in the circulant network $C_n(1,2)$ are finite and are bounded by the order of the network. Among the numerous implications of these findings are those that refer to the design and optimization of distributed sensor networks, improving communication and network protocols, as well as tracking the spread of infectious diseases and epidemics over social networks. The application of the identified methodology helps improve the process of network optimization which contributes to the development of more effective and robust circulant-based structures.