Computer-Organization
October 5, 2023GATE 2023
October 5, 2023UGC NET CS 2015 Dec- paper-2
| Question 2 |
Which of the following statement(s) is/are false ?
(a) A connected multigraph has an Euler Circuit if and only if each of its vertices has even degree.
(b) A connected multigraph has an Euler Path but not an Euler Circuit if and only if it has exactly two vertices of odd degree.
(c) A complete graph (K n ) has a Hamilton Circuit whenever n ≥ 3.
(d) A cycle over six vertices (C 6 ) is not a bipartite graph but a complete graph over 3 vertices is bipartite.
(a) A connected multigraph has an Euler Circuit if and only if each of its vertices has even degree.
(b) A connected multigraph has an Euler Path but not an Euler Circuit if and only if it has exactly two vertices of odd degree.
(c) A complete graph (K n ) has a Hamilton Circuit whenever n ≥ 3.
(d) A cycle over six vertices (C 6 ) is not a bipartite graph but a complete graph over 3 vertices is bipartite.
| (a) only | |
| (b) and (c) | |
| (c) only | |
| (d) only |
Question 2 Explanation:
(a)TRUE: A connected multigraph has an Euler Circuit if and only if each of its vertices has even degree.
(b)TRUE: A connected multigraph has an Euler Path but not an Euler Circuit if and only if it has exactly two vertices of odd degree.
(c)TRUE: A complete graph (K n ) has a Hamilton Circuit whenever n ≥ 3.
(d) FALSE: A cycle over six vertices (C 6 ) is not a bipartite graph but a complete graph over 3 vertices is bipartite.
(b)TRUE: A connected multigraph has an Euler Path but not an Euler Circuit if and only if it has exactly two vertices of odd degree.
(c)TRUE: A complete graph (K n ) has a Hamilton Circuit whenever n ≥ 3.
(d) FALSE: A cycle over six vertices (C 6 ) is not a bipartite graph but a complete graph over 3 vertices is bipartite.
Correct Answer: D
Question 2 Explanation:
(a)TRUE: A connected multigraph has an Euler Circuit if and only if each of its vertices has even degree.
(b)TRUE: A connected multigraph has an Euler Path but not an Euler Circuit if and only if it has exactly two vertices of odd degree.
(c)TRUE: A complete graph (K n ) has a Hamilton Circuit whenever n ≥ 3.
(d) FALSE: A cycle over six vertices (C 6 ) is not a bipartite graph but a complete graph over 3 vertices is bipartite.
(b)TRUE: A connected multigraph has an Euler Path but not an Euler Circuit if and only if it has exactly two vertices of odd degree.
(c)TRUE: A complete graph (K n ) has a Hamilton Circuit whenever n ≥ 3.
(d) FALSE: A cycle over six vertices (C 6 ) is not a bipartite graph but a complete graph over 3 vertices is bipartite.