finding if simple graph exists from a given degree sequence (undirected graph)

  1. The degree sequence of a simple graph is the sequence of the degrees of the nodes in the graph in decreasing order. Which of the following sequences can not be the degree sequence of any graph?
    I. 7, 6, 5, 4, 4, 3, 2, 1
    II. 6, 6, 6, 6, 3, 3, 2, 2
    III. 7, 6, 6, 4, 4, 3, 2, 2
    IV. 8, 7, 7, 6, 4, 2, 1, 1

(A) I and II
(B) III and IV
© IV only
(D) II and IV

1.please tell how to find if the given degree sequence forms a graph …!!

@bhanu1993 : A sequence for which a simple graph exists is called a graphical sequence or graphic sequence .

Erdos Gallai theorem characterizes such graphical sequences

Havel Hakimi algorithm can help you construct such a graph

You can read about these at wikipedia

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