On the Lovász Number of Certain Circulant Graphs

Exact formulae for the Lovász Theta Function of sparse Circulant Graphs

On the one-shot zero-error classical capacity of classical-quantum channels assisted by quantum non-signalling correlations

Duan and Winter studied the one-shot zero-error classical capacity of a quantum channel assisted by quantum non-signalling correlations, and formulated this problem as a semidefinite program depending only on the Kraus operator space of the channel. For the class of classical-quantum channels, they showed that the asymptotic zero-error classical capacity assisted by quantum non-signalling corre...

On the spectral Ádám property for circulant graphs

We investigate a certain condition for isomorphism between circulant graphs (known as the Ad am property) in a stronger form by referring to isospectrality rather than to isomorphism of graphs. We describe a wide class of graphs for which the Ad am conjecture holds. We apply these results to establish an asymptotic formula for the number of non-isomorphic circulant graphs and connected circulan...

The lower bound for the number of 1-factors in generalized Petersen graphs

‎In this paper‎, ‎we investigate the number of 1-factors of a‎ ‎generalized Petersen graph $P(N,k)$ and get a lower bound for the‎ ‎number of 1-factors of $P(N,k)$ as $k$ is odd‎, ‎which shows that the‎ ‎number of 1-factors of $P(N,k)$ is exponential in this case and‎ ‎confirms a conjecture due to Lovász and Plummer (Ann‎. ‎New York Acad‎. ‎Sci‎. ‎576(2006)‎, ‎no‎. ‎1‎, ‎389-398).

On the Enumeration of Circulant Graphs of Prime Power and Square Free Orders

The aim of this work is twofold: to unify, systematize and extend the known results of the analytical (i.e. formula-wise) counting of directed and undirected circulant graphs with a prime or, more generally, square-free number of vertices; to develop a general combinatorial framework for the counting of nonisomorphic circulant graphs with pk vertices, p odd prime, k 2. The general problem of co...