Confusion about the definition of an acyclic graph A graph is acyclic if it does not contain a cycle With that said, a directed graph is one where the edges are all endowed with a direction Associated with every digraph is its underlying graph which is an undirected graph with the same vertex and edge set but "ignoring" the direction
abstract algebra - Acyclic vs Exact - Mathematics Stack Exchange Mariano, you seem to be confusing a few things here A complex is acyclic if and only if it is exact (see for instance Exercise 1 1 5 in Weibel's Homological Algebra book, or probably anyplace where this is defined) An object is acyclic for a functor if the derived functors of said functor vanish on the object For instance a flasque sheaf
bipartite graph vs. directed acyclic graph - Mathematics Stack Exchange A directed acyclic graph need not be bipartite, and a directed bipartite graph need not be acyclic For example, the graph on 3 vertices with directed edges $\{v_1 \rightarrow v_2, v_1 \rightarrow v_3, v_2 \rightarrow v_3\}$ is a directed acyclic graph, but is not bipartite
coloring - Prove that number of acyclic orientations of a graph is the . . . There are two steps to the proof: proving that the number of acyclic orientations satisfies the deletion-contraction recurrence, and proving that (up to a factor of $(-1)^n$) it agrees with the chromatic polynomial evaluated at $-1$ on some base cases
definition - What is a directed acyclic graph (DAG)? - Mathematics . . . Therefore I would call what you drew a "directed acyclic multigraph" However, the reasoning for why how you draw it does not affect whether it is a DAG, as explained in Henning Makholm's answer, seems to have answered the question that you actually wanted to ask
category theory - derived functor through acylic resolution . . . Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers