Morphisms on Marked Graphs

On the Concrete Categories of Graphs

In the standard Category of Graphs, the graphs allow only one edge to be incident to any two vertices, not necessarily distinct, and the graph morphisms must map edges to edges and vertices to vertices while preserving incidence. We refer to these graph morphisms as Strict Morphisms. We relax the condition on the graphs allowing any number of edges to be incident to any two vertices, as well as...

Palindromic sequences generated from marked morphisms

Fixed points u = φ(u) of marked and primitive morphisms φ over arbitrary alphabet are considered. We show that if u is palindromic, i.e., its language contains infinitely many palindromes, then some power of φ has a conjugate in class P. This class was introduced by Hof, Knill and Simon (1995) in order to study palindromic morphic words. Our definitions of marked and well-marked morphisms are m...

Monads on Composition Graphs

Collections of objects and morphisms that fail to form categories inas-much as the expected composites of two morphisms need not always be deened have been introduced in 14, 15] under the name composition graphs. In 14, 16], notions of adjunction and weak adjunction for composition graphs have been proposed. Building on these deenitions, we now introduce a concept of monads for composition grap...

On morphisms of crossed polymodules

‎In this paper‎, ‎we prove that the category of crossed polymodules (i.e‎. ‎crossed modules of polygroups) and their morphisms is finitely complete‎. ‎We‎, ‎therefore‎, ‎generalize the group theoretical case of this completeness property of crossed modules‎.

Counting List Homomorphisms and Graphs with Bounded Degrees