Periodicity of Generalized Fibonacci-like Sequences

Graph Theoretical Models of Discrete Spaces with Locally Non-spherical Topology

“…Paper [11] shows that a graph theoretical model of a continuous closed n-dimensional manifold is a digital ndimensional surface with a locally-spherical topology. This means that in various applications and theories involving orientable and non-orientable continuous closed n-dimensional manifolds, these surfaces can be replaced by their graph theoretical models.…”

“…According to this definition and definition 6, a digital nsurface with a locally spherical topology is a digital nmanifold. As shown in [11], the graph theoretical model of a continuous closed n-dimensional manifold is necessarily a digital n-dimensional manifold. Several questions arise from this result, like what objects can be continuous counterparts of digital n-dimensional surfaces with a locally non-spherical topology.…”

“…Paper [11] proves that the intersection graph of any LCL cover of a continuous closed n-dimensional manifold is necessarily a digital n-dimensional manifold preserving global and local topological features of its continuous counterpart.…”

“…Digital n-dimensional spaces with a locally spherical topology are graph theoretical models of continuous n-dimensional spaces as it is shown in [7,11]. We discuss the particular case when the graph is a digital n-dimensional surface with a locally non-spherical topology.…”