5 papers
Fundamental Groupoids for Graphs
Tien Chih, Laura Scull
In this paper, we develop a -homotopy fundamental groupoid for graphs, and show a functorial relationship to the 2-category of graphs. We further explore the fundamental gr…
A Homotopy Category for Graphs
Tien Chih, Laura Scull
We show that the category of graphs has the structure of a 2-category with homotopy as the 2-cells. We then develop an explicit description of homotopies for finite graphs, in term…
The Fundamental Morphism Theorem in the Categories of Graphs & Graph Reconstruction
Tien Chih, Demitri Plessas
The Fundamental Morphism Theorem is a categorical version of the First Noether Isomorphism Theorem for categories that do not have kernels or cokernels. We consider two categories…
Graphs and Their Associated Inverse Semigroups
Tien Chih, Demitri Plessas
Directed graphs have long been used to gain understanding of the structure of semigroups, and recently the structure of directed graph semigroups has been investigated resulting in…
Generalized Affine Programming & Duality Gap with non-Division Rings
Tien Chih
Classical primal-dual affine programming takes place over finite dimensional real vector spaces. This results in beautiful duality theory, connecting the optimal solu- tions of the…