Independent sets,cliques and hamiltonian graphs

LetG be ak-connected (k 2) graph onn vertices. LetS be an independent set ofG. S is called essential if there exist two distinct vertices inS which have a common neighbor inG. LetV _r, be a clique which is a complete subgraph ofG. In this paper it is proven that if every essential independent setS ofk + 1 vertices satisfiesS V _r , thenG is hamiltonian, orG{u} is hamiltonian for someu V _r, orG is one of three classes of exceptional graphs. Our theorem generalizes several well-known theorems.     

Observation of isomeric states in197Bi

The high spin states of¹¹⁹Te, populated in¹¹⁰Pd(¹³C,4n) and¹¹⁰Pd(¹²C,3n) reactions, have been studied through -ray spectroscopy. The level scheme has been established upto a spin of 55/2. Three-quasiparticle states, based on g² _7/2h_11/2 and g_7/2d_5/2h_11/2 configurations, have been identified. The 35/2 and 39/2 states are suggested to be the fully aligned states constituted by five valence h_11/2 ³, g_7/2, d_5/2 quasiparticles.