Let G be a nontrivial connected graph of order n, and k an integer with 2 ≤ k ≤ n. For a set S of k vertices of G, let κ(S) denote the maximum number l of edge-disjoint trees T1, T2, . . . , Tl in G such that V (Ti) ∩ V (Tj) = S for every pair i, j of distinct integers with 1 ≤ i, j ≤ l. Chartrand et al. generalized the concept of connectivity as follows: The k-connectivity, denoted by κk(G), o...

1 Network System Research Institute, National Institute of Information and Communications Technology, 4-2-1 Nukui-kita, Koganei, Tokyo 184-8795, Japan 2 WPI Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan 3 Earth-Life Science Institute, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8550, Japan...

chaos theory discusses unstable and non-periodic behavior of non-linear fluctuating dynamicsystems. since evaporation level variations of lakes have a dynamic identity, chaos theory can have a uniquerole in collecting data of these variations. therefore it is an important and challenging problem in the field ofplanning and qualitative and quantitative management of urmia lake to verify whether ...

Recently, searching large-bulk band gap topological insulator (TI) is under intensive study. Through k·P theory and first-principles calculations analysis on antimonene, we find that α-phase antimonene can be tuned to a 2D TI under an in-plane anisotropic strain and the magnitude of direct bulk band gap (SOC gap) depends on the strength of spin-orbit coupling (SOC) which is strain-dependent. As...