The sphericity sph(G) of a graph G is the minimum dimension d for which G is the intersection graph of a family of congruent spheres in Rd . The edge clique cover number (G) is the minimum cardinality of a set of cliques (complete subgraphs) that covers all edges of G. We prove that if G has at least one edge, then sph(G) (G). Our upper bound remains valid for intersection graphs defined by bal...

We prove that the complex of proper non-trivial non-degenerate subspaces of a finitedimensional vector space endowed with a non-degenerate sesquilinear form is homotopy equivalent to a wedge of spheres. Additionally, we show that the same is true for a slightly wider class of simplicial complexes, the so-called generalized Phan geometries of type An. These generalized Phan geometries occur as r...

investigating downstream changes in bed load shape can be useful to detect watershedhydrological processes and it is very important to design hydraulic structures and to managecapacity of large storage dams, properly. regarding to doing of enforcement studies, thisresearch was conducted in qalesar river in upstream of chahardangeh watershed in mazandaranprovince. after recognition of the study ...