Anonymous asked in Science & MathematicsMathematics · 7 years ago

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

1 Answer

  • jibz
    Lv 6
    7 years ago
    Favorite 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.

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