On graphs with distinct vertex transmissions

Transmission of a vertex in a connected graph is the sum of distances from that vertex to all other vertices in the graph. While the use of transmissions as the basis for various topological indices is well known in mathematical chemistry, it is less known that transmissions have been used since 1970s also in space syntax, a particular field of architecture, to denote how easily one can get the sense of a whole building from a locally visible information. Besides these two applications, in this talk we will focus on recent theoretical results on transmissions in graphs, that are mostly related to questions of Klavžar and Dobrynin about graphs in which vertices have distinct transmissions.

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