###### Computer-Organization

October 5, 2023###### Computer-Networks

October 5, 2023# UGC 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

(d) A cycle over six vertices (C

(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

(d) FALSE: A cycle over six vertices (C

(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

(d) FALSE: A cycle over six vertices (C

(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. Subscribe

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