Let G be a finite non-abelian group and denote by Z(G) its center. The non-commuting graph of on transversal the center is whose vertices are non-central elements in two x y adjacent whenever xy=yx. In this work, we classify groups centeris double-toroidal or 1-planar.

We investigate under which conditions a mixed state on a finite-dimensional multipartite quantum system may be the unique, globally stable fixed point of frustration-free semigroup dynamics subject to specified quasi-locality constraints. Our central result is a linear-algebraic necessary and sufficient condition for a generic (full-rank) target state to be frustration-free quasi-locally stabil...

Abstract The daily commuting out of the city residence for labor purposes is a complex phenomenon driven by various geographical, transportation, economic, and social forces. Due to its high level complexity, current modeling approaches are mainly disciplinary thus lack multifaceted approach incorporating diverse conceptualization this phenomenon. To contribute demand, paper develops methodolog...

Let G be a group. The power graph of G is a graph with the vertex set G, having an edge between two elements whenever one is a power of the other. We characterize nilpotent groups whose power graphs have finite independence number. For a bounded exponent group, we prove its power graph is a perfect graph and we determine its clique/chromatic number. Furthermore, it is proved that for every grou...

The commuting graph C(G,X) , where G is a group and X a subset of G, has X as its vertex set with two distinct elements of X joined by an edge when they commute in G. Here the diameter and disc structure of C(G,X) is investigated when G is the symmetric group and X a conjugacy class of G.

We consider the entanglement properties of ground states of Hamiltonians which are sums of commuting projectors (we call these commuting projector Hamiltonians), in particular whether or not they have “trivial” ground states, where a state is trivial if it is constructed by a local quantum circuit of bounded depth and range acting on a product state. It is known that Hamiltonians such as the to...