For a given graph G having v vertices and e edges which is connected and has no cycles, which of the following statements is true?Group of answer choicesv = e+1v=ev + 1 = ev = e-1
Question
For a given graph G having v vertices and e edges which is connected and has no cycles, which of the following statements is true?Group of answer choicesv = e+1v=ev + 1 = ev = e-1
Solution
The correct statement is "v = e+1".
This is because a graph G that is connected and has no cycles is a tree. In a tree, the number of vertices (v) is always one more than the number of edges (e). This is a fundamental property of trees in graph theory.
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