The degree sequence of a tree is (1,1,...,1,2,3,4,4,5). Determine the number of 1's in the sequence.?
Math graph theory
- jibzLv 67 years agoFavorite Answer
Let v be the number of vertices in the tree. So v is the number of terms in the degree sequence. So v-5 is the number of 1s in the degree sequence. If we add up all the terms, we count every edge twice. Since this is a tree, the number of edges is v-1. Thus
(v-5)(1) + 2 + 3 + 4 + 4 + 5 = 2(v-1).
Hence v = 15.