Mongolian Tent Graph

A Mongolian tent graph is defined as the graph obtained from the grid graph  for odd  by adding an extra vertex above the graph and joining every other vertex of the top row to the additional vertex (Lee 1985; Gallian 2011, p. 14).

The -Mongolian tent graph is isomorphic to the 3-gear graph.

Mongolian tent graphs are graceful (Lee 1985, Gallian 2018).

Mongolian tent graphs are unit-distance for at least , , and  (E. Weisstein, Jul. 12, 2020).

A Mongolian village is defined as a graph formed by successively amalgamating copies of Mongolian tents with the same number of rows so that adjacent tents share a column (Gallian 2018).

Precomputed properties of Mongolian tent graphs are implemented in the Wolfram Language as GraphData["MongolianTent", m, n].

REFERENCES

Gallian, J. "Dynamic Survey of Graph Labeling." Elec. J. Combin. DS6. Dec. 21, 2018.

 https://www.combinatorics.org/ojs/index.php/eljc/article/view/DS6.Lee, S. M. "-Graceful Labelling of Mongolian Tents and Related Graphs." Congr. Numer. 50, 85-96, 1985.