# GATE | Sudo GATE 2020 Mock I (27 December 2019) | Question 19

The line graph L(G) of graph G has a vertex for each edge of G, and two of these vertices are adjacent iff the corresponding edges in G have a common vertex. Then which of the following option is false ?**(A)** Eulerian cycles of a graph G translate into Hamiltonian cycles of L(G).**(B)** If an edge has a vertex of degree d1 at one end and a vertex of degree d2 at the other, then (d1+d2) will be the degree of its corresponding vertex in the line graph.**(C)** If a graph G is regular of degree d, then L(G) will be regular line graph of degree 2(d-1).**(D)** None of these.**Answer:** **(B)****Explanation:** If an edge has a vertex of degree d1 at one end and a vertex of degree d2 at the other, then (d1+d2 – 2) will be the degree of its corresponding vertex in the line graph.

So, option (B) is false.

Quiz of this Question

Attention reader! Don’t stop learning now. Practice GATE exam well before the actual exam with the subject-wise and overall quizzes available in **GATE Test Series Course**.

Learn all **GATE CS concepts with Free Live Classes** on our youtube channel.