The image displays four distinct graphs, each labeled accordingly:**Graph 1**: This is a bipartite graph with two sets of nodes. Each node in the first set is connected to every node in the second set. The left set has four nodes, and the right set has three nodes, resulting in twelve edges.**Graph 2**: This consists of two disconnected components. Each component is a triangle, indicating three nodes with each node connected to the other two.**Graph 3**: This features two disconnected components as well. The left component includes three nodes with two connected by an edge. The right component is similar to those in Graph 2—a triangle with each node connected to the other two.**Graph 4**: Shaped like an "H", this graph is composed of five nodes. The central node connects to both left and right nodes, which each also connect to an additional node, forming a symmetrical structure.These visual representations illustrate different configurations of nodes and edges, commonly used in studies of graph theory. **Transcription:**7) What is the number of Hamilton circuits in K₁₅?**Explanation:**This question asks about the number of Hamiltonian circuits in the complete graph K₁₅. A Hamiltonian circuit is a closed loop on a graph where every node (vertex) is visited exactly once before returning to the starting node.In a complete graph Kₙ, where there are n vertices, the number of Hamiltonian circuits can be calculated using the formula:\[\frac{(n-1)!}{2}\]For K₁₅:\[\frac{(15-1)!}{2} = \frac{14!}{2}\] This calculates the number of unique tours possible in the graph. Since each tour can be traversed in reverse, we divide by 2 to avoid counting each circuit twice.

We know that Hamiltonian circuit is a circuits that visits every vertex exactly once except the…

Answered: What is the number of Hamilton circuits…

Math

Advanced Math

What is the number of Hamilton circuits in K15?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

A company that builds homes advertises that, by choosing from its upgrade options, each of its new homes is available in 512 different variations. How many upgrade options does the company offer?
An instructor gives an exam with twenty questions. Students are allowed to choose any fifteen questions to answer. (a) How many different choices of fifteen questions are there? (b) Suppose nine questions require coding and eleven do not. (i) How many groups of fifteen questions contain seven that require coding and eight that do not? (ii) How many groups of fifteen questions contain at most eight that require coding? (c) Suppose the exam instruction specifies that at most one of questions 1 and 2 MAY BE included among the fifteen. How many different choices of fifteen questions are there? (d) Suppose the exam instruction specifies that either both questions 1 and 2 are to be included among the ten or neither is to be included. How many different choices of ten questions are there?
A lock uses 3 numbers as an unlock code, each of which can be 0 to 19. If there are no restrictions on the numbers, how many possible unlock codes are available?
The student body of 135 students wants to elect two representatives. This is an example of [Select] n = [Select] r= [Select] There are [Select] ways to choose two representatives from the student body.
A number in Z+is written on the back of each of three cards. The numbers are not necessarily different but the sum of the three numbers is 14. Each card is flipped backwards so that the number cannot be seen by anyone. Carter, Mars, and Mann each select one of the cards, being careful not to let the other two see the number that is on the card. Carter says, after looking at his card, “I know that Mars and Mann have different numbers.” Mars then says, “I already knew that thet hree cards had different numbers.” At this point, Mann confidently exclaims, “I now know all thet hree numbers!” What were the numbers and who had which number?
To use an automated teller machine at a certain bank, you must enter a 5-digit code, using the digits 1–9. How many 5-digit codes are possible if repetition of digits is permitted?
11) Evaluate the following problem: 311five – 24five - MacBook Pro
A burger chain wants to send codes for a free small drink to the members of its kids club. The coupon code will have one letter, followed by two digits, followed by two letters. The letters R , S , T , and U and the digit 3 will not be used. So, there are 22 letters and 9 digits that will be used. Assume that the letters and digits can be repeated. How many such coupon codes can be generated?
Seven people are standing in a row. How many ways can they permute themselves so that at most two of them are in their original positions after the switch? (Note: the answer is Not 12,600)