Question

What is the Pru ̈fer code for a simple path whose vertices are numbered in increasing

order (i.e., 1 ∼ 2 ∼ 3 ∼ · · · ∼ n)?

Answer 1

Given that the vertices are numbered in Pncreasing order from 1 to n . The sequence will be having n-2 values. - The tree with vertices from 1 ton (Exitos) is as shown below and the prefercode will be having (0-2) = (5-2) = 3 values 2 3 initially the prufer code will be empty. Pruter code = { } Nowe Staut with the lowest label :say Q. Consider 2 as the lowest label in the above tree. find the Vertices connectiong it to the rest of the tree ay be in this case it is connected to 1. Now remove "a" from the tree and add b to prufer code. Prufer code = {13 Now, tree becomes

process, untill we are - and add it is connected to prufer code. 1 Continue the same above left two nodes. Now the lowest label is 3 1. so remove 3 and add 1 prufer code = {11} Now, tree becomes, it is connected prefer code to Now, the lowest label is 1. and 5. so remove land add 5 to pruter code = $111,53 Nowi toee becomes Stop the process now because we left with only 2 node si Therefore, the prefer code will be prufercode = {1,1,5}