Stepwise transmission irregular graphs

摘要

The distance d(u, v) between vertices u and v of a connected graph G is defined as the number of edges in a shortest path connecting them. The transmission of a vertex v of G is the sum of distances from v to all the other vertices of G. A graph is stepwise transmission irregular (STI) if the transmissions of any two of its adjacent vertices differ by exactly one. Some basic properties of STI graphs are established and infinite families are constructed.