Logout Open In App
Open In App
Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

Chapter 11: Q28SE (page 805)

Is a tree necessarily a cactus?

Short Answer

Expert verified

Therefore, the tree is a cactus.

Step by step solution

01

General form

Definition of tree: A tree isa connected undirected graph with no simple circuits.

Definition of Circuit: It is a path that begins and ends in the same vertex.

Definition of rooted tree: A rooted tree is a tree in which one vertex has been designated as the root and every edge is directed away from the root.

Definition of Cactus: A cactus is a connected graph in which no edge is in more than one simple circuit not passing through any vertex other than its initial vertex more than once or its initial vertex other than at its terminal vertex(where two circuits that contain the same edges are not considered different).

02

Evaluate the tree is cactus or not

A tree is a cactus, because a tree is a connected graph.

And a tree contains no simple circuits, which implies that no edge can be present in more than one simple circuit of the tree.

Conclusion: So, a tree is a cactus.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Which of these are well-formed formulae over the symbols \(\left\{ {{\bf{x,y,z}}} \right\}\) and the set of binary operators \(\left\{ {{\bf{ \ast , + ,}} \circ } \right\}\)?

  1. \({\bf{ \ast + + xyx}}\)
  2. \( \circ {\bf{xy \ast xz}}\)
  3. \({\bf{ \ast }} \circ {\bf{xz \ast \ast xy}}\)
  4. \({\bf{ \ast + }} \circ {\bf{xx}} \circ {\bf{xxx}}\)

Extend the definition of well-formed formulae in prefix notation to sets of symbols and operators where the operators may not be binary.

Show that there is a unique minimum spanning tree in a connected weighted graph if the weights of the edges are all different.

Show that when given as input an undirected graph with \(n\) vertices, no more than \(\left\lfloor {\frac{n}{{{2^k}}}} \right\rfloor \) trees remain after the first step of Sollin's algorithm has been carried out and the second step of the algorithm has been carried out \({\bf{k - 1}}\) times.

a) Define a full \(m{\bf{ - }}\)ary tree.

b) How many vertices does a full \(m{\bf{ - }}\)ary tree have if it has \({\bf{i}}\) internal vertices\(?\) How many leaves does the tree have?
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Pure Maths

Read Explanation

Decision Maths

Read Explanation

Mechanics Maths

Read Explanation

Logic and Functions

Read Explanation

Discrete Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free