Question

In a simple regular graph, total degree is 28. If the graph has more than one cycle in it, then the degree of each vertex is

• A. 2
• B. 4
• C. 7
• D. 14

Hint:

Use handshaking lemma: sum of degrees = \(2E\).

Answer 1

The Correct Option is B

Concept: \[ \text{Sum of degrees} = n \times k = 28 \]

Step 1: Possible values.
\[ nk = 28 \]

Step 2: Check condition.
Graph with more than one cycle $\Rightarrow$ degree \(k \ge 2\) Valid case: \[ n=7,\; k=4 \]