Problem of the Week 1209

Shoesmith Labelings

A Shoesmith labeling of a graph with E edges and V vertices is a labeling of the edges and vertices with distinct integers from 1 to V + E so that the label of every edge is either the sum or difference of the labels at its end.

The n-wheel W(n) is an n-vertex graph consisting of a regular (n − 1)-gon with a central vertex (hub) adjacent to all polygon vertices.

Here is a Shoesmith labeling of W(5):

Find a Shoesmith labeling of W(6).

Source: Ian Anderson, Magic polygons and Shoesmith labellings, Bull. ICA 74 (2015) 103-112.

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