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Results tagged with circulant-matrices
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user 10035
A circulant matrix is a square matrix where each row has the same elements as the previous row, cyclically rotated right by one element. It is a specific kind of a square Toeplitz matrix.
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Is this general form of Lovasz theta function of circulant graphs?
Let $G$ be a cirulant graph with no loops at vertices and vertex degree $d$. Is the Lovasz theta function of this graph given by:
$\vartheta(G) = \max_{i}\frac{-N\epsilon_{i}}{-\epsilon_{i}+d-1}$?
wh …
- 13.9k
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answer
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Partial Vandermonde circulant determinant expression
Consider following partial Vandermonde type, circulant matrix
$\begin{bmatrix}
x_1 & x_2 & 0 & \dots & 0 & x_n\\
x_1^2 & x_2^2 & x_3^2 & \dots & 0 & 0\\
\vdots &\vdots &\vdots &\ddots &\vdots &\vdots …
- 13.9k
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Lovász theta and circulant graphs
Let $\theta(G)$ denote the Shannon zero error capacity of graph $G$ and $\vartheta(G)$ be the Lovász upper bound for $\theta(G)$.
Let $C_{2n+1}$ denote the cycle graph with $2n+1$ nodes.
We know the f …
- 13.9k