# Questions tagged [signed-graphs]

In the area of graph theory in mathematics, a signed graph is a graph in which each edge has a positive or negative sign. A signed graph is balanced if the product of edge signs around every cycle is positive.

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### Is there always going to be both a concave up and down?

Throughout YouTube, I've seen people solve concavity and inflection questions where they find both: concave up and concave down. I was wondering if there were any instances where there was only one of ...
91 views

### Invariance of eigenvalues of a $0,\pm1$ matrix

Suppose that $G$ is a signed graph (a graph in which each edge has a positive of negative sign) Define Adjacency matrix of $G$ as before except that we have $+1$ for positive edges and $-1$ Prove ...
37 views

### What make a graph 3-balanced but not 4-balanced and locally balanced and global balanced?

$1)$ A signed graph $G$ is N-balanced if every circuit of length at most N is positive. Give an example of a signed graph which is 3-balanced but not 4 balanced? I tried drawing a square and made it ...
95 views

### What do you call a graph where the vertices are signed?

Let $G = (V, E)$ be a graph, and $f: V \to \{1,-1\}$ be a function assigning a sign to each vertex. What is this system $(G, f)$ called? In my current research, we've been using "oriented graph" to ...
243 views

### Intuitive explation for oriented matroids?

Where can you find intuitive explanation on oriented matroids? Other perhaps relevant questions on this How do you get the chirotope of a oriented matroid from the signed circuits? (other than just ...
### Signed complete graph with all cycles of length $k$ positive
A $\textit{signed graph}$ is a graph $G$ whose edges are signed either $+$ or $-$. A cycle is $\textit{positive}$ if the product of its edge signs is positive, i.e., it has an even number of ...