A directed graph is a graph with directed edges. Loops and 2-cycles are usually allowed. See also the tag *quiver*.

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When does the induced directed graph of a directed multigraph preserve information?

Let G be a directed multigraph, and let H be the induced directed graph whose vertices are the edges of G, and whose edges are given by pairs of consecutive edges in G; i.e., there is an edge from v ...
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Inverse (in)degree of a digraph

Hi All, here is my question. I'm given a directed graph $(V,E)$ with $|V| = n$ vertices and in-degrees $d_1$, $d_2$ ... $d_n$ (so that $\sum_i d_i = |E|$). Can we upper bound the inverse (in)degree ...
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“Box Nodes” in Directed Graphs with Paired IO Symmetry

Consider directed graphs where all nodes have 2 inputs and 2 outputs. If we design a box with N inputs and N outputs, what is the smallest number of nodes it must contain to satisfy “pair symmetry” ...
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A counterexample to a conjecture of Nash-Williams about hamiltonicity of digraphs?

Maybe I am missing something, but found potential counterexample to a conjecture of Nash-Williams. According to HAMILTONIAN DEGREE SEQUENCES IN DIGRAPHS The outdegree and indegree sequences of ...
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265 views

Minimum spanning subgraph with at least one incoming and one outgoing edge

Given a single-component, directed acyclic graph with one source (vertex with only outgoing edges) and one sink (vertex with only incoming edges), I'd like to find a minimum spanning subgraph which ...
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222 views

Minimum number of edges - directed graph with given sums of weights

Let's consider a directed graph with positive edge weights. For every vertex we determine the difference D = (summary weight of edges directed FROM this vertex)-(summary weight of edges directed ...
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182 views

Ihara zeta function (graph theory) coefficients using a line graph

I'VE COMPLETELY REVISED MY QUESTION I wish to take a simple undirected graph (i.e. the complete graph K_4) Arbitrarily direct said graph, and then create a line graph from the directed version of ...
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113 views

When can we make a digraph acyclic by fliping groups of arcs?

We have a digraph D=(V,A) and its arc set A is partitioned into classes. We can flip the classes, which means changing the direction of all the arcs in the class. Is there any result on when can we ...
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Majority vote of total orders

Fix an odd natural number $k$. Suppose we have $k$ total orders on the same (finite) set $X$. Define a tournament on the vertex set $X$ by putting a directed edge $x\rightarrow y$ if a majority of ...
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396 views

Algebraic characterisation of directed acyclic graphs

Any characterization based on the adjacency matrix for directed acyclic graphs (DAG)? An undirected graph could be simply characterized by saying that its adjacency matrix is symmetric. What about a ...
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Is number of quasi-kernels NP-hard?

A quasi-kernel in a directed graph D is an independent subset of vertices $S$ so that for every $v \in V(D)-S$ either $v->s$ for some $s \in S$ or $v->w->s$ for some $w \in V(D)-S, s \in S$. ...