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Let $G$ be a graph on $n$ vertices with $4n-16$ edges.Consider the following:
1. There is a vertex of degree smaller than $8$ in $G.$

2. There is a vertex such that there are less than $16$ vertices at a distance exactly $2$ from it.

Which of the following is TRUE:

  1.  1 only
  2. 2 only
  3.  Both 1 and 2
  4.  Neither 1 nor 2
in Graph Theory by Active
edited by | 189 views
I think only 1 is true..
Is it option a?
Yes. Please explain. Unable to understand the given 2nd statement.
please elaborate its solution..

1 Answer

0 votes
For 1 use sum of vertex degree = twice the number of edges

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