Bicompleteness in the Category of Partial Graphs with Total Homomorphisms

Category Theory is becoming an useful tool to formalize abstract concepts making easy to construct proofs and investigate properties while graphs are commonly used to model systems. Partiality is a important mathematical concept used in Mathematics and Computer Science. In this paper we define a category where objects are partial graphs whose arcs may have source and/or target nodes undefined and morphisms are total homomorphisms o