Complementary descriptions of Euler characteristics of simplicial incidence pseudographs

Abstract We introduce incidence pseudographs and simplicial incidence pseudographs with a poset topology, which provide discrete representation of continuous objects and helpful tools in digital image analysis. We prove closed or open sub-pseudograph matching theorems in a regular incidence pseudograph. By embedding a finite simplicial incidence pseudograph into an optimal simplicial incidence pseudograph, we obtain several formulae which give complementary descriptions of Euler characteristics of finite simplicial incidence pseudographs and its relative pseudographs. These descriptions provide new methods of calculating Euler characteristics by boundary counts rather than all nodes and make it possible, in some cases, to simplify the complexity of computing Euler characteristic of finite simplicial incidence pseudographs.