 14.1.14.1.1: A finite set of points connected by line segments is called a(n) .
 14.1.14.1.2: A point in a graph is called a(n) .
 14.1.14.1.3: A line segment in a graph is called a(n) .
 14.1.14.1.4: An edge that connects a vertex to itself is called a(n) .
 14.1.14.1.5: A sequence of adjacent vertices and the edges connecting them is ca...
 14.1.14.1.6: A path that begins and ends with the same vertex is called a(n) .
 14.1.14.1.7: The number of edges that connect to a vertex is called the of the v...
 14.1.14.1.8: A bridge is an edge that, if removed from a connected graph, would ...
 14.1.14.1.9: In Exercises 914, create a graph with the given properties. There a...
 14.1.14.1.10: In Exercises 914, create a graph with the given properties. There a...
 14.1.14.1.11: In Exercises 914, create a graph with the given properties. There a...
 14.1.14.1.12: In Exercises 914, create a graph with the given properties. There a...
 14.1.14.1.13: In Exercises 914, create a graph with the given properties. There a...
 14.1.14.1.14: In Exercises 914, create a graph with the given properties. There a...
 14.1.14.1.15: In Exercises 1520, use the graph below to answer the following ques...
 14.1.14.1.16: In Exercises 1520, use the graph below to answer the following ques...
 14.1.14.1.17: In Exercises 1520, use the graph below to answer the following ques...
 14.1.14.1.18: In Exercises 1520, use the graph below to answer the following ques...
 14.1.14.1.19: In Exercises 1520, use the graph below to answer the following ques...
 14.1.14.1.20: In Exercises 1520, use the graph below to answer the following ques...
 14.1.14.1.21: Modified Knigsberg Bridge In Exercises 21 and 22, suppose that the ...
 14.1.14.1.22: Modified Knigsberg Bridge In Exercises 21 and 22, suppose that the ...
 14.1.14.1.23: Other Navy Regions In Exercises 23 and 24, the maps of states that ...
 14.1.14.1.24: Other Navy Regions In Exercises 23 and 24, the maps of states that ...
 14.1.14.1.25: Central America The map below shows the countries of Belize (B ), C...
 14.1.14.1.26: Northern Africa The map below shows the countries of Algeria (A ), ...
 14.1.14.1.27: For Exercises 2730, use a graph to represent the floor plan shown. ...
 14.1.14.1.28: For Exercises 2730, use a graph to represent the floor plan shown. ...
 14.1.14.1.29: For Exercises 2730, use a graph to represent the floor plan shown. ...
 14.1.14.1.30: For Exercises 2730, use a graph to represent the floor plan shown. ...
 14.1.14.1.31: Representing a Neighborhood The map of the Tree Tops subdivision in...
 14.1.14.1.32: Representing a Neighborhood The map of the Crescent Lakes subdivisi...
 14.1.14.1.33: In Exercises 3336, determine whether the graph shown is connected o...
 14.1.14.1.34: In Exercises 3336, determine whether the graph shown is connected o...
 14.1.14.1.35: In Exercises 3336, determine whether the graph shown is connected o...
 14.1.14.1.36: In Exercises 3336, determine whether the graph shown is connected o...
 14.1.14.1.37: In Exercises 37 40, a connected graph is shown. Identify any bridge...
 14.1.14.1.38: In Exercises 37 40, a connected graph is shown. Identify any bridge...
 14.1.14.1.39: In Exercises 37 40, a connected graph is shown. Identify any bridge...
 14.1.14.1.40: In Exercises 37 40, a connected graph is shown. Identify any bridge...
 14.1.14.1.41: Poll your entire class to determine which students knew each other ...
 14.1.14.1.42: Attempt to draw a graph that has an odd number of odd vertices. Wha...
 14.1.14.1.43: Draw four different graphs and then for each graph: a) determine th...
 14.1.14.1.44: Facebook Friends Read the Recreational Mathematics box on page 855....
 14.1.14.1.45: Use a graph to represent a) the floor plan of your home. b) the str...
 14.1.14.1.46: Choose a continent other than North America or Australia and create...
Solutions for Chapter 14.1: Graph Theory
Full solutions for A Survey of Mathematics with Applications  9th Edition
ISBN: 9780321759665
Solutions for Chapter 14.1: Graph Theory
Get Full SolutionsA Survey of Mathematics with Applications was written by Patricia and is associated to the ISBN: 9780321759665. Chapter 14.1: Graph Theory includes 46 full stepbystep solutions. Since 46 problems in chapter 14.1: Graph Theory have been answered, more than 22936 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: A Survey of Mathematics with Applications, edition: 9. This expansive textbook survival guide covers the following chapters and their solutions.

Adjacency matrix of a graph.
Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected). Adjacency matrix of a graph. Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected).

Affine transformation
Tv = Av + Vo = linear transformation plus shift.

Augmented matrix [A b].
Ax = b is solvable when b is in the column space of A; then [A b] has the same rank as A. Elimination on [A b] keeps equations correct.

Big formula for n by n determinants.
Det(A) is a sum of n! terms. For each term: Multiply one entry from each row and column of A: rows in order 1, ... , nand column order given by a permutation P. Each of the n! P 's has a + or  sign.

Block matrix.
A matrix can be partitioned into matrix blocks, by cuts between rows and/or between columns. Block multiplication ofAB is allowed if the block shapes permit.

Change of basis matrix M.
The old basis vectors v j are combinations L mij Wi of the new basis vectors. The coordinates of CI VI + ... + cnvn = dl wI + ... + dn Wn are related by d = M c. (For n = 2 set VI = mll WI +m21 W2, V2 = m12WI +m22w2.)

Characteristic equation det(A  AI) = O.
The n roots are the eigenvalues of A.

Circulant matrix C.
Constant diagonals wrap around as in cyclic shift S. Every circulant is Col + CIS + ... + Cn_lSn  l . Cx = convolution c * x. Eigenvectors in F.

Factorization
A = L U. If elimination takes A to U without row exchanges, then the lower triangular L with multipliers eij (and eii = 1) brings U back to A.

Fundamental Theorem.
The nullspace N (A) and row space C (AT) are orthogonal complements in Rn(perpendicular from Ax = 0 with dimensions rand n  r). Applied to AT, the column space C(A) is the orthogonal complement of N(AT) in Rm.

GaussJordan method.
Invert A by row operations on [A I] to reach [I AI].

GramSchmidt orthogonalization A = QR.
Independent columns in A, orthonormal columns in Q. Each column q j of Q is a combination of the first j columns of A (and conversely, so R is upper triangular). Convention: diag(R) > o.

Hypercube matrix pl.
Row n + 1 counts corners, edges, faces, ... of a cube in Rn.

Kirchhoff's Laws.
Current Law: net current (in minus out) is zero at each node. Voltage Law: Potential differences (voltage drops) add to zero around any closed loop.

lAII = l/lAI and IATI = IAI.
The big formula for det(A) has a sum of n! terms, the cofactor formula uses determinants of size n  1, volume of box = I det( A) I.

Length II x II.
Square root of x T x (Pythagoras in n dimensions).

Linear transformation T.
Each vector V in the input space transforms to T (v) in the output space, and linearity requires T(cv + dw) = c T(v) + d T(w). Examples: Matrix multiplication A v, differentiation and integration in function space.

Projection p = a(aTblaTa) onto the line through a.
P = aaT laTa has rank l.

Vector space V.
Set of vectors such that all combinations cv + d w remain within V. Eight required rules are given in Section 3.1 for scalars c, d and vectors v, w.

Volume of box.
The rows (or the columns) of A generate a box with volume I det(A) I.
I don't want to reset my password
Need help? Contact support
Having trouble accessing your account? Let us help you, contact support at +1(510) 9441054 or support@studysoup.com
Forgot password? Reset it here