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.