A survey on automorphism groups and transmission-based graph invariants

The distance d(u,v) between vertices u and v of a simple connected graph G is equal to the number of edges in a minimal path connecting them. The transmission of a vertex v is defined by σ(v) = Σ u∈V(G) d(v,u). A graph invariant (topological index) is said to be a transmission-based topological index (TT index) if it includes the transmissions σ(u) of vertices of G. Because σ(u) can be derived from the distance matrix of G, it follows that transmission-based topological indices form a subset of distance-based topological indices. In this article we survey some results on the computation of some transmission-based graph invariants of intersection graph, hypercube graph, Kneser graph, Paley graph and unitary Cayley graph.