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Double-wheel Graphs

These graphs consist of two wheels, Wm, with a common hub. They could be composed as

  
The double wheel 2C5+K1 with a graceful labelling.

We have shown that 2C3+K1 is not graceful, whereas 2Cn+K1 is for 3 < n < 11. We have found the number of non-isomorphic graceful labellings for n = 4 and 5; it takes too long to find all graceful labellings for larger values of n.

Graph A graceful labelling Number of labellings
2C3+K1 - 0
2C4+K1 {0;1,3,16,12;5,14,8,15} 44
2C5+K1 {0;1,3,14,6,19;5,17,7,16,20} 1216
2C6+K1 {0;1,3,7,22,5,21;6,19,11,23,14,24} -
2C7+K1 {0;1,3,8,20,27,6,24;9,22,26,10,25,11,28} -
2C8+K1 {0;1,3,7,13,32,23,11,27;5,29,14,31,10,28,8,30} -
2C9+K1 {0;1,3,7,12,26,6,35,13,31;8,33,10,34,15,32,11,27,36} -
2C10+K1 {0;1,3,7,12,18,31,8,40,10,36;9,33,16,37,15,34,14,39,11,38} -


Next: Other wheel-based graphs Up: Introduction Previous: KmxPn graphs

Barbara Smith
January 2003