# Discrete Structures-Graph [NTA-NET (Based on NTA-UGC) Computer Science (Paper-II)]: Questions 1 - 3 of 37

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## Question number: 1

» Discrete Structures » Graph » Hamiltonian and Eulerian Graphs, Planar Graphs

Appeared in Year: 2013

### Question

Which of the following statement (s) is/are false?

- A connected multigraph has an Euler Circuit if and only if each of its vertices has even degree.
- A connected multigraph has an Euler Path but not an Euler Circuit if and only if it has exactly two vertices of odd degree.
- A complete graph (K
_{N}) has a Hamilton Circuit whenever n≥3 - A cycle over six vertices (C
_{6}) is not a bipartite graph but a complete graph over 3 vertices is bipartite. (Dec)

### Choices

Choice (4) | Response | |
---|---|---|

a. | (1) only | |

b. | (2) and (3) | |

c. | (3) only | |

d. | (4) only |

## Question number: 2

» Discrete Structures » Graph » Spanning Trees

Appeared in Year: 2015

### Question

A tree with n vertices is called graceful, if its vertices can be labelled with integers 1,2, …, n such that the absolute value of the difference of the labels of adjacent vertices are all different. Which of the following trees are graceful?

### Choices

Choice (4) | Response | |
---|---|---|

a. | (a) and (c) | |

b. | (b) and (c) | |

c. | (a), (b) and (c) | |

d. | (a) and (b) |

## Question number: 3

» Discrete Structures » Graph » Spanning Trees

Appeared in Year: 2016

### Question

The number of different spanning trees in complete graph, and bipartite graph have ………. and…. . …. respectively.

### Choices

Choice (4) | Response | |
---|---|---|

a. | 14,14 | |

b. | 16,4 | |

c. | 16,14 | |

d. | 14,4 |