If G=(VG,EG) is a graph of order n, we call S⊆VG an isolating set if the graph induced by VG−NG[S] contains no edges. The minimum cardinality of an isolating set of G is called the isolation number of G, and it is denoted by ι(G). It is known that ι(G)≤n3 and the bound is sharp. A subset S⊆VG is called dominating in G if NG[S]=VG. The minimum cardinality of a dominating set of G is the domination number, and it is denoted by γ(G)....

A set D of vertices of a graph G is isolating if the set of vertices not in D and with no neighbor in D is independent. The isolation number of G, denoted by \iota(G) , is the minimum cardinality of an isolating set of G. It is known that \iota(G) \leq n/3 , if G is a connected graph of order n, , distinct from C_5 . The main result of this work is the characterisation of unicyclic and block graphs of order n with isolating number...

Seismic isolation is identified as one of the most popular and effective methods of protecting structures under strong dynamic excitations. Base isolators, such as Lead Rubber Bearings, High Damping Rubber Bearings, and Friction Pendulum Bearings, are widely used in practice in many earthquake-prone regions of the world to mitigate structural vibrations, and therefore minimize loss of life and property damage during seismic events....

One of the methods in structural control is the application of combinational control systems in order to reduce the response of structures during earthquakes. The aim of the present paper is to verify the effectiveness of a hybrid control strategy, combining base isolation and non-traditional tuned mass dampers (TMDs) (i.e., TMDs with dashpots directly connected to the ground) in suppressing structural vibrations of high-rise buildings....

After the recent finding that CrI3, displays ferromagnetic order down to its monolayer, extensive studies have followed to pursue new two-dimensional (2D) magnetic materials. In this article, we report on the growth of single crystal CrCl3 in the layered monoclinic phase. The system after mechanical exfoliation exhibits stability in ambient air (the degradation occurs on a time scale at least four orders of magnitude longer than...