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Abstract
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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.
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