Purchase Solution

# Graceful Trees and Paths

Not what you're looking for?

A (p,q) graph G is called graceful if it is possible to label the vertices of G with distinct
elements from the set {0,1,...,q} in such a way that the induced edge labeling, which
assigns the integer |i - j| to the edge ij, assigns the labels 1,2,...,q to the q edges of G.
The graceful tree conjecture states that every tree is graceful.
a. Prove that every path is graceful.
b. Prove that every star K_(1,n) is graceful.
c. Show that every tree of order 6 is graceful.

##### Solution Summary

Graceful trees and paths are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

##### Solution Preview

There are some typos in the statement.
Here is a corrected text:
============================
A (p,q) graph G is called graceful if it is possible to label the vertices of G with distinct
elements from the set {0,1,...,p} in such a way that the induced edge labeling, which
assigns the integer |i - j| to the edge ij, assigns the labels 1,2,...,q to the q edges of G.
The ...

##### Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

##### Probability Quiz

Some questions on probability

##### Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

##### Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

##### Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.