Different labeling on a graph produces class of isomorphic graphs. Two isomorphic graphs possess similar characteristic such as connectivity, degree distribution of vertices, equality of spectrum and many others. I am looking for some properties of graph which depends particularly on vertex labeling. One such property is separability of the quantum state related to that graph. Depending on the vertex labeling two isomorphic graphs may generate different quantum states with different separability. Is there any other properties of graph which depends on vertex labeling only?