This paper provides new observations on the Lovász θ-function of graphs. These include a
simple closed-form expression of that function for all strongly regular graphs, together with …

In this paper, we present a fractional version of Haemers' bound on the Shannon capacity of
a graph, which is originally due to Blasiak. This bound is a common strengthening of both …

The orthogonality dimension of a graph $ G=(V, E) $ over a field $\mathbb {F} $ is the
smallest integer $ t $ for which there exists an assignment of a vector $ u_v\in\mathbb {F}^ t …

We define the relative fractional independence number of a graph $ G $ with respect to
another graph $ H $, as $$\alpha^*(G| H)=\max_ {W}\frac {\alpha (G\boxtimes W)}{\alpha …

The asymptotic spectrum of graphs, introduced by Zuiddam (Combinatorica, 2019), is the
space of graph parameters that are additive under disjoint union, multiplicative under the …

Shannon OR-capacity $ C_ {\rm OR}(G) $ of a graph $ G $, that is the traditionally more often
used Shannon AND-capacity of the complementary graph, is a homomorphism monotone …

This paper delves into three research directions, leveraging the Lovász ϑ-function of a
graph. First, it focuses on the Shannon capacity of graphs, providing new results that …

An orthogonal representation of a graph is an assignment of nonzero real vectors to its
vertices such that distinct non-adjacent vertices are assigned to orthogonal vectors. We …

The zero-error capacity of a noisy channel is defined as the least upper bound of rate at
which it is possible to transmit information with zero probability of error. It was posed by …

We define the “relative” fractional independence number of a graph G with respect to
another graph H, as where the maximum is taken over all graphs W., G\boxtimesW is the …