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 ...

The graph of y = f (x) where f (x) = x 2 is the same as the graph of y = x 2. Writing equations as functions in the form f (x) is useful when applying translations and reflections to graphs.

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 ...

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

Motivated by work of Yu.L. Shmul'yan a pre-order and an equivalence relation on the set of operator-valued Schur class functions are introduced and the behavior of Redheffer linear fractional ...