# 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.

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.

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