# Graph Parameters via Operator Systems

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## Abstract

This work is an attempt to bridge the gap between the theory of operator systems and various aspects of graph theory.

We start by showing that two graphs are isomorphic if and only if their corresponding operator systems are isomorphic with respect to their order structure. This means that the study of graphs is equivalent to the study of these special operator systems up to the natural notion of isomorphism in their category. We then define a new family of graph theory parameters using this identification. It turns out that these parameters share a lot in common with the Lov'{a}sz theta function, in particular we can write down explicitly how to compute them via a semidefinte program. Moreover, we explore a particular parameter in this family and establish a sandwich theorem that holds for some graphs.

Next, we move on to explore the concept of a graph homomorphism through the lens of C