Semigroups of transformations and endomorphisms have emerged as powerful algebraic frameworks to elucidate the underlying structures of graphs. By harnessing the principles of semigroup theory ...

GCSE Eduqas Transformation of curves - Higher - Eduqas Translating graphs Functions of graphs can be transformed to show shifts and reflections.

Learn how to use functions to represent translations, sketches, compressions and reflections of graphs with GCSE Bitesize Maths.

Functional data that are nonnegative and have a constrained integral can be considered as samples of one-dimensional density functions. Such data are ubiquitous. Due to the inherent constraints, ...

The approximation of the Ihara zeta function via the normalized version on finite graphs in the sense of Benjamini and Schramm follows as a special case. Our framework not only unifies corresponding ...