# Tagged Questions

**4**

votes

**1**answer

152 views

### How to find or constrain “particularly good” (two-sided) spectral expanders?

I'm new to graph theory, but a response to a question I asked a while ago introduced me to the concept of expander graphs.
A k-regular graph (henceforth "graph") on n nodes has eigenvalues k = λ1 ≥ ...

**5**

votes

**2**answers

238 views

### Number of trees with the same matching number

Let $\sigma(n,m)$ be the number of trees with $n$ vertices $\{ v_1, \dots, v_n \}$ such that the matching number (the size of a maximum matching) is $m$.
I have been trying to compute the value of ...

**2**

votes

**3**answers

460 views

### Non-isomorphic graphs with the same numbers of closed walks

Can somebody help me to construct two family of finite simple connected graph $G_i$ and $H_i$, $i=1, 2, \cdots,n$ ($n$ possibly large), such that:
$1)$ $G_i\ncong H_i$ for $i=1, 2, \cdots, n$
$2)$ ...