Transmission Dimension

Let G be a connected graph with vertex set V(G) and vertex transmission T(u) for u in V(G). The transmission dimension of G is the number of distinct vertex transmissions,

dim_T(G)=|{T(u):u in V(G)}|.

In particular, G is transmission-regular iff dim_T(G)=1.

See also

Graph Transmission, Transmission-Minimal Regular Graph, Transmission-Regular Graph, Vertex Transmission

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References

Alfaro, C. A.; Villagrán, R. R.; and Zapata, O. "Distinguishing Graphs with Two Integer Matrices." 27 Sep 2023. https://arxiv.org/abs/2309.15365.

Cite this as:

Weisstein, Eric W. "Transmission Dimension." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/TransmissionDimension.html

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