The vertex connectivity () G κ of a graph G is the minimum number of nodes whose deletion disconnects it. Graph connectivity is one of the most fundamental problems in graph theory. In this paper, we designed an () 2 O n time algorithm to solve connectivity problem on circular trapezoid graphs.

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We report generation of directional far-infrared emission between Rydberg states (s, p, f, and g Rydberg series) of NO in the gas phase initiated by the absorption of black body radiation at room temperature. All the transitions detected are assignable to the nf → (n – 1)g and n'g → (n' – 1)f transitions. The longest wavelength observed in the present experiment was ~ 112 µm (2.7 THz) which corresponds to the 14f → 13g transition. The laser-prepared population in the 14s and 15s states are transferred to the 13f and 14f states located energetically higher, respectively, which generates the subsequent emission of 13f → 14g at ~ 88 µm and 14f → 13g at ~ 112 µm. Collisions of Rydberg molecules with the surrounding ground state molecules are considered to responsible for the upward population flow. The population in the 14p and 15p states are transported to the 13f and 14f states located energetically lower, respectively, which gives rise to the subsequent emission of 13f → 12g at ~ 88 µm and 14f → 13g at ~ 112 µm.