In Exercises 7 through 20 you are given information about a network. Choose one

Question

In Exercises 7 through 20 you are given information about a network. Choose one of the following three options: (A) the network is definitely a tree; (B) the network is definitely not a tree; (C) the network may or may not be a tree (more in- formation is needed). Accompany your answer with a brief explanation for your choice. 7. The network has 15 vertices and 16 edges. 8. The network has 23 vertices and no bridges. 9. The network has 16 vertices and 15 edges. The network has 23 vertices and 22 bridges. 11. The network has redundancy R = 1. 13. The network has 10 vertices (A through J), and there is 14 The network has 10 vertices (A through J) and there 15. The network has five vertices, no loops, and no mul- 16. The network has five vertices, no loops, and no mul The network has redundancy R = 0. only one path connecting A and J. are two paths connecting C and D tiple edges, and every vertex has degree 4. tiple edges, and every vertex has degree 2

Explanation / Answer

8)the network has 23 vertices and no bridges

it is may not be a tree because depending on the number of edges it will be become a tree

10) the network has 23 vertices and 22 bridges

it is may or may not be a tree if all edges become a bridges then network become a tree

14)the network has 10 vertices and there is two paths between Cand D

it will not become a tree because a tree doesn't have any cycle if their is twompaths it will become a cycle then it will not become a tree

18)the network has no loops and no multiple edges and have two vertices has degree 1 and three has degree 2

this one become tree

20)the network has two vertices of odd degree and all ther vetices of even degree

here the network is may or may not be a tree because their is no details in this question

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