Skip to content
Related Articles

Related Articles

GATE | Quiz for Sudo GATE 2021 | Question 14
  • Last Updated : 15 Dec, 2020

The line graph L(G) of a simple graph G is defined as follows:

  • There is exactly one vertex v(e) in L(G) for each edge e in G.
  • For any two edges e and e’ in G, L(G) has an edge between v(e) and v(e’), if and only if e and e’are incident with the same vertex in G.

Which of following option(s) is/are correct about “Line Graph”?

Note – This question is multiple select questions (MSQ).
(A) A line graph has an articulation point if and only if the underlying graph has a bridge for which neither endpoint has degree one
(B) For a graph G with n vertices and m edges, the number of vertices of the line graph L(G) is m, and the number of edges of L(G) is half the sum of the squares of the degrees of the vertices in G, m.
(C) If a graph G has an Euler cycle, that is, if G is connected and has an even number of edges at each vertex, then the line graph of G is Hamiltonian.
(D) None of these


Answer: (A) (C)

Explanation: For a graph G with n vertices and m edges, the number of vertices of the line graph L(G) is m, and the number of edges of L(G) is half the sum of the squares of the degrees of the vertices in G, minus m.

Option (B) is false.

See properties of Line graph.


Quiz of this Question
Please comment below if you find anything wrong in the above post

My Personal Notes arrow_drop_up
Recommended Articles
Page :