A family of graphs generated by Hilbert space

In this paper, we introduce a novel class of graphs based on Hilbert spaces, termed Hilbert graphs. Constructed using the inner product defined on a Hilbert space, Hilbert graphs leverage the concept of orthogonality, where orthogonal elements correspond to adjacent vertices. We demonstrate that Hilbert graphs are regular and vertex transitive, with the clique number equal to the dimension of the corresponding Hilbert space. Our investigation encompasses various properties of Hilbert graphs, including connectivity, girth, diameter, and chromatic number, and we draw comparisons with Cayley graphs and zero divisor graphs.

کلیدواژه ها:

Hilbert Graph ، orthogonality ، regular graph ، vertex transitive graph