On quartic transmission irregular graphs

摘要

Distance between two vertices is the number of edges in a shortest path connecting them in a connected graph G. The transmission of a vertex v is the sum of distances from v to all the other vertices of G. If transmissions of all vertices are mutually distinct, then G is a transmission irregular graph. The following problem was posed by Alizadeh and Klavžar [Appl Math Comput 328 (2018) 113–118]: do there exist infinite families of regular transmission irregular graphs? In this paper, we construct an infinite family of 4-regular transmission irregular graphs.