Abstract:
In this paper, we introduce the reader to the graph labeling question in the setting of
quantum mechanics. We formally define an edge weight of a graph G and use it to develop the general labeling number. We derive some elementary results about this number and give an example of a quantum chromatic labeling function of a simple path graph of two vertices that is not replicable in the classical setting. We define a quantum labeling number for any graph and show that it is at most as large as the classical labeling number. Finally we posit a relationship between the quantum labeling numbers as seen in different tensor products of operator spaces common to Quantum Information Theory.