 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 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 61445 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.

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

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.

Complex conjugate
z = a  ib for any complex number z = a + ib. Then zz = Iz12.

Cyclic shift
S. Permutation with S21 = 1, S32 = 1, ... , finally SIn = 1. Its eigenvalues are the nth roots e2lrik/n of 1; eigenvectors are columns of the Fourier matrix F.

Diagonal matrix D.
dij = 0 if i # j. Blockdiagonal: zero outside square blocks Du.

Exponential eAt = I + At + (At)2 12! + ...
has derivative AeAt; eAt u(O) solves u' = Au.

Free variable Xi.
Column i has no pivot in elimination. We can give the n  r free variables any values, then Ax = b determines the r pivot variables (if solvable!).

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

Hermitian matrix A H = AT = A.
Complex analog a j i = aU of a symmetric matrix.

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

Left inverse A+.
If A has full column rank n, then A+ = (AT A)I AT has A+ A = In.

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.

Markov matrix M.
All mij > 0 and each column sum is 1. Largest eigenvalue A = 1. If mij > 0, the columns of Mk approach the steady state eigenvector M s = s > O.

Matrix multiplication AB.
The i, j entry of AB is (row i of A)·(column j of B) = L aikbkj. By columns: Column j of AB = A times column j of B. By rows: row i of A multiplies B. Columns times rows: AB = sum of (column k)(row k). All these equivalent definitions come from the rule that A B times x equals A times B x .

Multiplication Ax
= Xl (column 1) + ... + xn(column n) = combination of columns.

Norm
IIA II. The ".e 2 norm" of A is the maximum ratio II Ax II/l1x II = O"max· Then II Ax II < IIAllllxll and IIABII < IIAIIIIBII and IIA + BII < IIAII + IIBII. Frobenius norm IIAII} = L La~. The.e 1 and.e oo norms are largest column and row sums of laij I.

Row picture of Ax = b.
Each equation gives a plane in Rn; the planes intersect at x.

Spanning set.
Combinations of VI, ... ,Vm fill the space. The columns of A span C (A)!

Transpose matrix AT.
Entries AL = Ajj. AT is n by In, AT A is square, symmetric, positive semidefinite. The transposes of AB and AI are BT AT and (AT)I.