Vertex decomposability and regularity of very well-covered graphs

A graph $G$ is well-covered if it has no isolated vertices and all the maximal independent sets have the same cardinality. If furthermore two times this cardinality is equal to $|V(G)|$, the graph $G$ is called very well-covered. The class of very well-covered graphs contains bipartite well-covered graphs. Recently in \cite{CRT} it is shown that a very well-covered graph $G$ is Cohen-Macaulay if and only if it is pure shellable. In this article we improve this result by showing that $G$ is Cohen-Macaulay if and only if it is pure vertex decomposable. In addition, if $I(G)$ denotes the edge ideal of $G$, we show that the Castelnuovo-Mumford regularity of $R/I(G)$ is equal to the maximum number of pairwise 3-disjoint edges of $G$. This improves Kummini's result on unmixed bipartite graphs.Comment: 11 page

Lucio Parenzan: an appreciation

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<<A>> methodology for the development of autonomic and cognitive internet of things ecosystems

Dottorato di Ricerca in Information and Computation Technologies, Ciclo XXXAdvancements on microelectromechanical systems, embedded technologies, and wireless communications have recently enabled the evolution of conven- tional everyday things in enhanced entities, commonly de ned Smart Objects (SOs). Their continuous and widespread di usion, along with an increasing and pervasive connectivity, is enabling unforeseen interactions with conven- tional computing systems, places, animals and humans, thus fading the bound- ary between physical and digital worlds. The Internet of Things (IoT) term just refers to such futuristic scenario, namely a loosely coupled, decentralized and dynamic ecosystem in which bil- lions (even trillions) of self-steering SOs are globally interconnected becoming active participants in business, logistics, information and social processes. In- deed, SOs are able to provide highly pervasive cyberphysical services to both humans and machines thanks to their communication, sensing, actuation, and embedded processing capabilities. Nowadays, the systemic revolution that can be led through the complete realization of the IoT vision is just at its dawn. As matter of facts, whereas new IoT devices and systems have been already developed, they often result in poorly interoperating \Intra-nets of things", mainly due to the heterogeneity featuring IoT building blocks and the lack of standards. Thus, the develop- ment of massive scaled (the total number of \things" is forecasted to reach 20.4 billion in 2020) and actually interoperable IoT systems is a challenging task, featured by several requirements and novel, even unsurveyed, issues. In this context, a multidisciplinary and systematic development approach is necessary, so to involve di erent elds of expertise for coping with the cy- berphysical nature of IoT ecosystem. Henceforth, full- edged IoT methodolo- gies are gaining traction, aiming at systematically supporting all development phases, addressing mentioned issues, and reducing time-to-market, e orts and probability of failure. In such a scenario, this Thesis proposes an application domain-neutral, full- edged agent-based development methodology able to support the main engineering phases of IoT ecosystems. The de nition of such systematic approach resulted in ACOSO-Meth (Agent-based COoperating Smart Objects Methodology), which is the major contribution of this thesis along with other interesting research e orts supporting (i.e., a multi-technology and multi- protocol smartphone-based IoT gateway) and extending (i.e., a full- edged approach to the IoT services modeling according to their opportunistic prop- erties) the main proposal. Finally, to provide validation and performance eval- uation of the proposed ACOSO-Meth approach, four use cases (related to di erent application contexts such as a smart university campus, a smart dig- ital library, a smart city and a smart workshop) have been developed. These research prototypes showed the e ectiveness and e ciency of the proposed approach and improved their respective state-of-the-art. iiUniversità della Calabri