Conditional Strong Matching Preclusion of the Alternating Group Graph

The strong matching preclusion number of a graph is the minimum number of vertices and edges whose deletion results in a graph that has neither perfect matchings nor almost-perfect matchings. Park and Ihm introduced the problem of strong matching preclusion under the condition that no isolated vertex is created as a result of faults. In this paper, we find the conditional strong matching preclusion number for the $n$-dimensional alternating group graph $AG_n$

The Conditional Strong Matching Preclusion of Augmented Cubes

The strong matching preclusion is a measure for the robustness of interconnection networks in the presence of node and/or link failures. However, in the case of random link and/or node failures, it is unlikely to find all the faults incident and/or adjacent to the same vertex. This motivates Park et al. to introduce the conditional strong matching preclusion of a graph. In this paper we consider the conditional strong matching preclusion problem of the augmented cube $AQ_n$, which is a variation of the hypercube $Q_n$ that possesses favorable properties

Conditional Matching Preclusion for the Alternating Group Graphs and Split-Stars

The matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost-perfect matchings. For many interconnection networks, the optimal sets are precisely those induced by a single vertex. Recently, the conditional matching preclusion number of a graph was introduced to look for obstruction sets beyond those induced by a single vertex. It is defined to be the minimum number of edges whose deletion results in a graph with no isolated vertices that has neither perfect matchings nor almost-perfect matchings. In this article we find this number and classify all optimal sets for the alternating group graphs, one of the most popular interconnection networks, and their companion graphs, the split-stars. Moreover, some general results on the conditional matching problem are presented

A complex systems approach to education in Switzerland

The insights gained from the study of complex systems in biological, social, and engineered systems enables us not only to observe and understand, but also to actively design systems which will be capable of successfully coping with complex and dynamically changing situations. The methods and mindset required for this approach have been applied to educational systems with their diverse levels of scale and complexity. Based on the general case made by Yaneer Bar-Yam, this paper applies the complex systems approach to the educational system in Switzerland. It confirms that the complex systems approach is valid. Indeed, many recommendations made for the general case have already been implemented in the Swiss education system. To address existing problems and difficulties, further steps are recommended. This paper contributes to the further establishment complex systems approach by shedding light on an area which concerns us all, which is a frequent topic of discussion and dispute among politicians and the public, where billions of dollars have been spent without achieving the desired results, and where it is difficult to directly derive consequences from actions taken. The analysis of the education system's different levels, their complexity and scale will clarify how such a dynamic system should be approached, and how it can be guided towards the desired performance