Picture fuzzy graph, belonging to fuzzy graphs family, has good capabilities at times when we are faced with problems that cannot be expressed by fuzzy graphs and intuitionistic fuzzy graphs. When an element membership is not clear, neutrality is a good option that can be well-supported by a picture fuzzy graph. The previous definitions limitations in fuzzy graph energy have led us to offer new definitions in picture fuzzy graphs. In this article, we expanded the energy concept on the picture fuzzy graph and sought to use this concept in modeling issues related to this graph and solving some problems including the neutrality state. We were able to show that neutrality, as part of total energy, is effective in energy-based decisions. This is noticeable in some types of energy and is more pronounced. We were looking for a way to rank the available options using the picture fuzzy graph and its Laplacian energy/energy in decision making. We studied some types of energy including Laplacian and skew Laplacian in both picture fuzzy graphs and picture fuzzy digraphs, and discussed some of its properties. We discussed some energy boundaries in this graph, and finally, the applications of energy were presented.

DNA computing has gained considerable attention due to the characteristics of high-density information storage and high parallel computing for solving computational problems. Building addressable logic gates with biomolecules is the basis for establishing biological computers. In the current calculation model, the multiinput AND operation often needs to be realized through a multilevel cascade between logic gates. Through experiments, it was found that the multilevel cascade causes signal leakage and affects the stability of the system. Using DNA strand displacement technology, we constructed a domino-like multiinput AND gate computing system instead of a cascade of operations, realizing multiinput AND computing on one logic gate and abandoning the traditional multilevel cascade of operations. Fluorescence experiments demonstrated that our methods significantly reduce system construction costs and improve the stability and robustness of the system. Finally, we proved stability and robustness of the domino AND gate by simulating the tic-tac-toe process with a massively parallel computing strategy.

DNA computing has become the focus of computing research due to its excellent parallel processing capability, data storage capacity, and low energy consumption characteristics. DNA computational units can be precisely programmed through the sequence specificity and base pair principle. Then, computational units can be cascaded and integrated to form large DNA computing systems. Among them, DNA strand displacement (DSD) is the simplest but most efficient method for constructing DNA computing systems. The inputs and outputs of DSD are signal strands that can be transferred to the next unit. DSD has been used to construct logic gates, integrated circuits, artificial neural networks, etc. This review introduced the recent development of DSD-based computational systems and their applications. Some DSD-related tools and issues are also discussed.

Self-assembled DNA nanostructures significantly contribute to DNA nanotechnology.

The advent of fuzzy sets, and consequently fuzzy graphs, has solved many problems in ambiguous and uncertain contexts. It is interesting and necessary to study the Wiener index in a cubic fuzzy graph that employs both fuzzy membership and interval-valued fuzzy membership at the same time. In this paper, the Wiener index in a cubic fuzzy graph is introduced as a cubic fuzzy number and some related results are described. The comparison between connectivity index and Wiener index, changes in Wiener index through deleting a node or an edge, and determining the Wiener index in some specific cubic fuzzy graphs have been the other topics studied in this research. In addition, the Wiener index is determined by mentioning concepts of the saturated cubic fuzzy cycle. In this review, the Wiener index is shown as a combination of classical and interval numbers. The results indicate that when some vertices are removed, the Wiener index may change. However, this change will not be exclusively related to both values. Finally, an application of the Wiener index is presented in the study of the properties of some monomer molecules.