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I have been working with the chromatic polynomials of circulant graphs of prime order $p$ with two distinct parameters, i.e. $P_{p,i,j}(x):= P(C_{p}(i,j),x)$ with $1 \leq i \neq j \leq \ n/2.$ In ...

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 ...

The cycle has this property. For instance, the distance matrix for a 6-cycle is: $A=\begin{bmatrix} 0 & 1 & 2 & 3 & 2 & 1 \\\\ 1 & 0 & 1 &...

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: $\vartheta(G) = \max_{i}\frac{-N\epsilon_{i}}{-\epsilon_{i}+d-1}$? ...