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In many fields, including science, technology, engineering, and communication networks, the idea of domination is used. Double domination is a widely recognized idea of domination concept in graph theory. A prominent crucial factor in network architecture is integrity. A subset $S$ of $V(G)$ is called a double dominating set of $G$ if each vertex of $G$ is dominated at least twice by $S$. In this paper, an algorithm to compute the double domination integrity of graphs is given. Also, an application of double domination integrity in the optimal phasor measurement unit placement problem in a power system is given.

While B2C via cloud computing has grown rapidly, information security and trustworthy computation are still major issues in today’s industrial realm. As a result, the routine workflow process varies dynamically over the course of data transactions, resulting in uncertainty. Consumers’ private information becomes easily vulnerable due to such data uncertainty. Intruders/fake marketers may permeate deeply into their current profiles due to the Internet, which leads to the creation of fictitious online markets that, in turn, drive more demand. This evolving business interaction leverages new interlopes to target customers’ data more precisely. However, it is still lacking in terms of complete techniques for dealing with such issues. These days, uncertain B2C workflows are greatly aided by Blockchain technology, especially to most of its security-enhancing characteristics. Despite numerous existing studies that have recommended employing Blockchain to handle B2C records, it is necessary to employ the technology in such business sectors to offer secured record management, workflow and keep data with high confidentiality and integrity intact. In this study, we suggest a Distributed Decentralized Security Scheme (DDSS) that manages and secures uncertain datasets through Blockchain technology in the B2C sector. To improve the safety of data workflows, the proposed approach enables the user to verify the authenticity of the records they require. A smart contract or special chain-code is used to dictate the parameters of the suggested system, ensuring security. The findings and discussions explain that the suggested scheme is far more effective than the previous strategies and has a greater level of confidentiality and integrity strength.

Spanness of fuzzy graph is introduced. By spanness, a new vulnerability parameter, span integrity is defined in fuzzy graph. The span integrity values are found for path, cycle, complete fuzzy graph, complete bipartite fuzzy graphs. Path and cycle with node strength sequence are discussed. Brain network is modeled as a fuzzy graph and Span integrity is applied to the brain network. Span integrity of fuzzy brain network is calculated for before and after meditation models. The results are compared and the improvement in the stability of the brain network is shown.