Topic: Discrete Mathematics
Which of the following are true?
(i) In a graph G with 'n' vertices and 'e' edges, sum of degrees of vertices = 2*e
(ii) Eccentricity of a connected graph can never be equal to radius of the graph
(iii) Girth of a graph is the total number of edges in the shortest cycle of the graph
(iv) Graph with equal degree for all vertices is multigraph
- A. (i), (ii), (iii)
- B. (ii), (iii), (iv)
- C. (i), (iii), (iv)
- D. None of the above
Answer: D. None of the above
Explanation: Statement (i) is true (Handshaking lemma). Statement (ii) is false; the radius is defined as the minimum eccentricity among all vertices. Statement (iii) is true. Statement (iv) is false; a graph with equal degrees is a regular graph, not necessarily a multigraph. Since no option perfectly lists just (i) and (iii), (d) is the correct choice.