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The International Institute of Knowledge Innovation and Invention (IIKII) is an institute that promotes the exchange of innovations and inventions, and establishes a communication platform for international innovations and researches. In 2019, IIKII cooperated with the Institute of Electrical and Electronics Engineers (IEEE) Tainan Section Sensors Council to hold IEEE conferences such as IEEE ICIASE 2019, IEEE ECBIOS 2019, IEEE ICKII 2019, ICUSA-GAME 2019, and IEEE ECICE 2019. This Special Issue entitled "Selected Papers from IIKII 2019 conferences" aims to select excellent papers from IIKII 2019 conferences, including symmetry in physics, chemistry, biology, mathematics, and computer science, etc. It selected 21 excellent papers from 750 papers presented in IIKII 2019 conferences on the topic of symmetry. The main goals of this Special Issue are to encourage scientists to publish their experimental and theoretical results in as much detail as possible, and to discover new scientific knowledge relevant to the topic of symmetry. [ABSTRACT FROM AUTHOR]

Graphs are often used as models to solve problems in computer science, mathematics, and biology. A pancake sorting problem is modeled using a pancake graph whose classes include burnt pancake graphs, signed permutation graphs, and restricted pancake graphs. The network cost is degree × diameter. Finding a graph with a small network cost is like finding a good sorting algorithm. We propose a novel recursively divided pancake (RDP) graph that has a smaller network cost than other pancake-like graphs. In the pancake graph Pn, the number of nodes is n!, the degree is n − 1, and the network cost is O(n2). In an RDPn, the number of nodes is n!, the degree is 2log2n − 1, and the network cost is O(n(log2n)3). Because O(n(log2n)3) < O(n2), the RDP is superior to other pancake-like graphs. In this paper, we propose an RDPn and analyze its basic topological properties. Second, we show that the RDPn is recursive and symmetric. Third, a sorting algorithm is proposed, and the degree and diameter are derived. Finally, the network cost is compared between the RDP graph and other classes of pancake graphs. [ABSTRACT FROM AUTHOR]