# Tagged Questions

0answers
26 views

### The lower bound of Cheeger Inequality as the degree goes to infinity

Consider an undirected graph $G(V,E)$ with adjacency matrix $A$ and define the graph Laplacian as $$L = D - A$$ where $D$ is a diagonal matrix such that $D(i,i) = d_i$. ...
1answer
42 views

### Can this famous theorem extended to the weighted undirected graphs?

There is well-known bound on the largest eigenvalue of graphs that says $$\sqrt{d_{max}}\leq \lambda_{max}$$. Is it also true for weighted graphs? (Where as usual, the degree of a vertex in a weighted ...
1answer
20 views

### Is there any weighted graph which smallest eigenvalue of its adjacency matrix is greater than 1?

Is there any weighted or unweighted graph which smallest eigenvalue of its adjacency matrix is greater than 1?
1answer
175 views

### Two formulas for the minimal eigenvalue of a graph

Hello again everybody, I'm reading Fan Chung's monograph Spectral Graph Theory. In it, she has two formulas for the minimal eigenvalue of a graph. She doesn't explain why they're equivalent, and I'm ...
1answer
449 views

### What does the minimal eigenvalue of a graph say about the graph's connectivity?

I'm reading Fan Chung's Spectral Graph Theory, and I'm now in chapter 2. There, Chung proves Cheeger's inequality, which is that $2h_G \geq \lambda_1 > h_G^2/2$ for any graph $G$. To me, this ...
1answer
243 views