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In order to make a full evaluation of an interconnection network, it is essential to estimate the minimum size of a largest connected component of this network provided the faulty vertices in the network may break its connectedness. Star graphs are recognized as promising candidates for interconnection networks. This article addresses the size of a largest connected component of a faulty star graph. We prove that, in an n-star graph (n ≥ 3) with up to 2n − 4 faulty vertices, all fault-free vertices but at most two form a connected component. Moreover, all fault-free vertices but exactly two form a connected component if and only if the set of all faulty vertices is equal to the neighbourhood of a pair of fault-free adjacent vertices. These results show that star graphs exhibit excellent fault-tolerant abilities in the sense that there exists a large functional network in a faulty star graph.

A novel radix-3/9 algorithm for type-III generalized discrete Hartley transform (GDHT) is proposed, which applies to length-3p sequences. This algorithm is especially efficient in the case that multiplication is much more time-consuming than addition. A comparison analysis shows that the proposed algorithm outperforms a known algorithm when one multiplication is more time-consuming than five additions. When combined with any known radix-2 type-III GDHT algorithm, the new algorithm also applies to length-2q3p sequences.

Advances in information and communication technologies have created a range of new products and services for the well-being of society. Virtual Reality (VR) technology has shown enormous potential in educational, commercial, and medical fields. The recent COVID-19 outbreak highlights a poor global performance in communicating epidemic knowledge to the public. Considering the potential of VR, the research starts from analyzing how to use VR technology to improve public education in COVID-19. The research uses Virtual Storytelling Technology (VST) to promote enthusiasm in user participation. A Plot-based VR education system is proposed in order to provide an immersive, explorative, educational experiences. The system includes three primary modules: the Tutorial Module, the Preparation Module, and the Investigation Module. To remove any potential confusion in the user, the research aims to avoid extremely complicated medical professional content and uses interactive, entertainment methods to improve user participation. In order to evaluate the performance efficiency of the system, we conducted performance evaluations and a user study with 80 participants. Compared with traditional education, the experimental results show that the VR education system can used as an effective educational tool for epidemic (COVID-19) fundamental knowledge. The VR technology can assist government agencies and public organizations to increase public understanding of the spread the epidemic (COVID-19).

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