Infinite family of transmission irregular trees of even order

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. It is known that almost no graphs are transmission irregular. Infinite families of transmission irregular trees of odd order were presented in Alizadeh and Klavžar (2018). The following problem was posed in Alizadeh and Klavžar (2018): do there exist infinite families of transmission irregular trees of even order? In this article, such a family is constructed.