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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.
How far from their shore is their enemies catapult? Are their shots too short or too long to hit us and by how much?
interpreting graphs we often use graphs of recent data to project the changes in future data. the following is the
Problem on transportation
The number of motor vehicles deaths increased by 13.75 times from 1912 to 2003. There were 39,525 more deaths in 2003 than in 1912. Find the number of motor vehicle deaths in each of the two years.
write an equation in slope intercept form for the line that passes through the given point and is parallel to the graph
Explain the general relationship between abstract algebra and linear algebra and dscuss how it is possible to considerably shorten the list of properties that define a vector space by using definitions from abstract algebra.
the width of a rectangular painting is 3in. more than twice the height. a frame is 2.5 in. wide goes around the
Draw the line AB that passes through these points - what is the value of the slope and what is the value of the x-intercept?
Compute the age of the older friend.
For the rational expression (x^2-1) / (x+1)^2, the domain of this is expression is?
Use the echelon method to solve the system of three equations in three unknowns. Determine the equation of the line described. Put the answer in the slope -intercept form, if possible. Through (-7,-7), parallel to 5x-4y=-19
Calculating the function values
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