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Prüfer codes and palindroms
Task number: 4238
Suppose we have a spanning tree \( T \) of a complete graph with an even number of vertices, whose Prüfer code is a palindrome. Prove that the tree \( T \) does not contain vertices of even degrees.
A palindrome is a string that contains the same numbers when reading it forward as well as backwards. For example 1,1,2,2,1,1; 1,2,3,2,1 and 3,12,7,7,12,3 are palindromes.