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

learn more… | top users | synonyms

4
votes
1answer
125 views

Directed homotopy in the Cayley graph of a monoid

There is a the notion of the Cayley graph $C(G)$ of a group $G$ (which depends on a given presentation $G \cong \mathcal F(S) / \sigma$ where $\mathcal F$ is the free group functor and $\sigma$ some ...
9
votes
1answer
90 views

A generalisation of $C_0$-semigroups

A $C_0$-semigroup is a strongly continuous family $\{T(t)\}$ of bounded linear operators on a normed space $X$, indexed in $\mathbb R_+$ and with two additional properties that make it look like an ...
0
votes
0answers
30 views

Variant of Directed-Force Graph

I have an idea for a variant of the directed-force graph (a "DFG" for short). It seems so obvious to me that I feel certain someone has already developed it but I am a computer geek, not a ...
3
votes
0answers
94 views

Does this notion of “$\mathcal{F}$-digraph” appear in the literature?

By a digraph, I mean a quiver with no multiple edges. So in particular: Loops are okay. An infinite set of vertexes is okay. Furthermore, I will tend to identify each digraph with its underlying ...
4
votes
0answers
44 views

Digraph weak connectivity in $O(V)$ space and $O(V+E)$ time

A digraph is called weakly connected if its underlying undirected graph is connected. You are given a digraph $G$ with $V$ vertices and $E$ edges as a read-only data structure consisting of lists of ...
0
votes
1answer
112 views

Petersen 2-factor decomposition theorem for directed graphs

Petersen proved that every 2k-regular graph can be decomposed into k disjoint 2-factors. I would like to know that is it true that if G is a directed regular graph (d_out(v)=d_in(v)=k), then can G be ...
2
votes
0answers
104 views

Properties of a smallest tournament with domination number $k$

For some tournament $T$, let $\gamma(T)$ denote the cardinality of a smallest dominating set of $T$. Denote by $f(k)$ the minimum number of vertices of a tournament $T$ having $\gamma(T) = k$. From ...
1
vote
0answers
114 views

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 ...
1
vote
0answers
155 views

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 ...
0
votes
0answers
79 views

“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” ...
8
votes
0answers
362 views

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 ...
1
vote
1answer
457 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 ...
0
votes
1answer
507 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 ...
1
vote
2answers
244 views

Ihara zeta function (graph theory) coefficients using a line graph [closed]

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 ...
5
votes
1answer
132 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 ...
5
votes
4answers
278 views

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 ...
4
votes
1answer
732 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 ...
1
vote
2answers
162 views

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 $w \in V(D)-S, s \in S$. ...