Triangular Snake Graph
المؤلف:
Clancy, K.; Haythorpe, M.; and Newcombe, A
المصدر:
§4.5.1 in "A Survey of Graphs with Known or Bounded Crossing Numbers." 15 Feb 2019, pp. 58-59. https://arxiv.org/abs/1901.05155.
الجزء والصفحة:
...
19-5-2022
2106
Triangular Snake Graph
The triangular snake graph 
is the graph on 
vertices with 
odd defined by starting with the path graph 
and adding edges 
for 
, ..., 
. The first few are illustrated above, and special cases are summarized in the following table.
 |
 |
| 1 |
singleton graph  |
| 3 |
triangle graph  |
| 5 |
butterfly graph |
Triangular snakes are unit-distance and matchstick by construction, perfect. They are graceful when the number of triangles is congruent to 0 or 1 (mod 4) (Moulton 1989, Gallian 2018), which is equivalent to when 
. Triangular snakes are also geodetic.
REFERENCES
Clancy, K.; Haythorpe, M.; and Newcombe, A. §4.5.1 in "A Survey of Graphs with Known or Bounded Crossing Numbers." 15 Feb 2019, pp. 58-59. https://arxiv.org/abs/1901.05155.
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.
Moulton, D. "Graceful Labelings of Triangular Snakes." Ars Combin. 28, 3-13, 1989.
Rajan, B.; Rajasingh. I.; and Vasanthi Beulah, P. "Crossing Number of Join of Triangular Snake with 
." Path and Cycle. Int. J. Comp. Appl. 44, 20-22, 2012.
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