The degree-sequence tag has no wiki summary.

**6**

votes

**1**answer

160 views

### Smallest Connected Graph for Given Degree Sequence

For a given integer sequence $(d_1, d_2,...,d_n)$, a natural question is if such a sequence is graphical, i.e. is a degree sequence of some graph. According to Erdős–Gallai theorem, A sequence of ...

**4**

votes

**1**answer

180 views

### Graphs with constant edge imbalance

The imbalance of an edge $(u,v) \in E(G)$ of a graph $G$ is defined as $|d(u)-d(v)|$ ($d$ being, as usual the degree). (This concept was introduced by Albertson in 1997)
I'm interested in the set of ...

**1**

vote

**1**answer

163 views

### Have you come across this kind of “degree” concept?

Let $A \subseteq V(G)$ be a set of vertices in a graph $G$ and let $v \in V(G)$ be some vertex. Define $d_{A}(v)$ as the number of neighbours of $v$ inside $A$.
Now suppose you have a graph whose ...