The incidence matrix of a directed graph G = (V, E) is a |V| Ã |E| matrix

Question:

The incidence matrix of a directed graph G = (V, E) is a |V| Ã— |E| matrix B = (bij) such that

Describe what the entries of the matrix product B BT represent, where BT is the transpose of B.

-1 if edge j leaves vertex i. if edge j enters vertex i. h. otherwise.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Discrete and Combinatorial Mathematics An Applied Introduction

ISBN: 978-0201726343

5th edition

Authors: Ralph P. Grimaldi

See More Books

Question Posted: Jul 13, 2010 12:07 PM

See More Questions

The adjacency list representation of a directed graph G is given by the lists in Table 7.6. Construct G from this representation. st 14558000 1 2 3 4 5 6 7 8 1236334536 7-a le d 1 2 3 4 5 6 7 8 9
A path cover of a directed graph G = (V, E) is a set P of vertex-disjoint paths such that every vertex in V is included in exactly one path in P. Paths may start and end anywhere, and they may be of...
The graph in Prob. 8, incidence Matrix of a Digraph; Matrix B = [bkj] with entries find the incidence matrixof; bjk 1 0 if edge e leaves vertex j if edge e enters vertex j otherwise.
A mail-order firm processes 5,300 checks per month. Of these, 60 percent are for $55 and 40 percent are for $80. The $55 checks are delayed two days on average; the $80 checks are delayed three days...
The following relative frequency ogive represents the lengths of a random sample of tornadoes in the United States. (a) What is the class width? (b) Approximately 92% of all tornadoes are less than...
What considerations should be given to a message recipients culture when planning a good-news or neutral-news message?
a. Are the quadratic terms important? Consider a linear model of LNEXPENSES on 12 explanatory variables. For the explanatory variables, include assets, GROUP, both versions of losses and gross...
The comparative balance sheet of Canace Products Inc. for December 31, 2016 and 2015, is as follows: The income statement for the year ended December 31, 2016, is as follows: Additional data obtained...
Estimate the 5 - day 9 9 % VaR for the portfolio assuming that its annual volatility calculated on the basis of weekly returns from the most recent 1 - year time window is 3 1 . 7 5 % .
In its accrual-basis income statement for the year ended December 31, 2014, Dart Company reported revenue of $1,750,000. Additional information follows: Accounts receivable 12/31/13...
When an adjacency-matrix representation is used, most graph algorithms require time (V2), but there are some exceptions. Show that determining whether a directed graph G contains a universal sink-a...
Let G = (V, E) be an undirected, connected graph with weight function w : E R, and suppose that |E| |V| and all edge weights are distinct. A second-best minimum spanning tree is defined as follows....
Can you think of something that is legal but unethical, or something that is ethical, but illegal?
Based only on the material found in our textbook, please answer the following questions: (1) Describe and discuss the performance evaluation process. (2) What is standard deviation, the Sharpe ratio,...
Select one specific financial institution or financial market and relate the history in that area to the development of current regulations. Cover the major legislations that resulted and how...
How much must you invest today at 10% interest in order to see your investment grow to $8,000 in 3 years? To save for a new car, Samuel will invest $18,000 at the end of each year for the next 5...
Consider the CAPM. The expected return market is 20%. The expected return on a stock with a beta of 1.2 is 22%. What is the risk free rate?
F is an all-equity firm with assets worth $1Mns. Expected returns on assets equal to 9%. F buys new assets at market value for $0.5Mns (same risk as existing assets). The acquisition is financed by...
$x_{1}=371, n_{1}=509, x_{2}=434, n_{2}=579,95 \%$ confidence Construct a confidence interval for $p_{1}-p_{2}$ at the given level of confidence.
Differentiate the following terms/concepts: a. Personality types and money attitudes b. Planners and avoiders c. Moderating and adapting to biases d. "Perfectible judges" and "incorrigible judges"
What is the economic reason why the SRAS curve slopes up?
6. Consider the following algorithm. Give a function with one term and coefficient 1 g(n) such that the running time of this algorithm is (g(n)), and briefly explain. public static int funkySum...
In the diagram, let U = {all objects}, B = {all students who live in Hartford}, = {students majoring in math}, and R = {students taking a course with Professor Antonio} B M 1 2 3 5 + 6 7 8 R In which...
Risk Identification: Disruption Disruption Assessment: Assessment: Risk Risk Probability Risk 1: Cyberwarfare 1 Consequence 5 Risk 2: Natural 1 5 Diaster Risk 3: Supplier 2 2 closure Risk 4:...

The incidence matrix of a directed graph G = (V, E) is a |V| Ã |E| matrix

Question:

-1 if edge j leaves vertex i. if edge j enters vertex i. h. otherwise.

Step by Step Answer:

BBT i j biebj bieb je e E e E If i j then biebje 1 it i...View the full answer

Discrete and Combinatorial Mathematics An Applied Introduction

Students also viewed these Computer Sciences questions