Intereting Posts

For any given function $f\colon \to\Bbb R$, what is $\int_0^1\frac{f(x)}{f(x)+f(1-x)}dx$?
If N is a normal subgroup of G,decide whether np(N) | np(G) or np(G/N) | np(G)?
How similarity transformation is related to coordinate transformation?
Distributing $k$ distinct items among $r$ distinct groups without ordering
Coupon Collector Problem – expected number of draws for some coupon to be drawn twice
A curious identity on sums of secants
How to find the sum $\displaystyle\sum^n_{k=1} (k^2+k+1)k!$
Why is an ellipse, hyperbola, and circle not a function?
Elementary solution of exponential Diophantine equation $2^x – 3^y = 7$.
Decreasing sequence of product $\sigma$-algebras
Math behind rotation in MS Paint
Why is $\pi$ = 3.14… instead of 6.28…?
How do I calculate a dihedral angle given Cartesian coordinates?
About irrational logarithms
Why is the ring of matrices over a field simple?

as i read the following text :

“Let P be a shortest path from some vertex s to some other vertex t in a graph. If the

weight of each edge in the graph is increased by one, P will still be a shortest path

from s to t”

Solution: False. the shortest path would change if 1 was added to every edge weight.

- easy to implement method to fit a power function (regression)
- What algorithm is used by computers to calculate logarithms?
- number of derangements
- Why does this algorithm to plot implicit equations work?
- Why does Strassen's algorithm work for $2\times 2$ matrices only when the number of multiplications is $7$?
- Calculation of Bessel Functions

I ran into a new question:

Suppose we have a Graph G in which weight of all edges is >1 (positive). If we increase weight of all edges by one, the shortest path between two specific vertex has the same edges.

I doubt about this question. would u please anyone clarify me?

- What is the best way to self-study GAP?
- Determining computational complexity of stochastic processes
- Quadratic sieve algorithm
- Largest idempotent
- Efficiently calculating the logarithmic integral with complex argument
- $k$ litres of Milk delivery with minimum cost
- Honest and Deceitful Professors Problem
- Why can't reachability be expressed in first order logic?
- An algorithm to convert float number to binary representation
- nth convolved Fibonacci numbers of order 6 modulo m

Let $G$ be the complete graph on three vertices $A,B,$ and $C$. Let edges $AB$ and $BC$ have weight $2$, and edge $AC$ have weight $4.5$.

Then the shortest path from $A$ to $C$ is via $B$. But if you increase the weights to $3,3,$ and $5.5$, the shortest path is the edge $AC$.

If you want integer weights, you can do it with four points, with edge weights $AB=BC=CD=2$, $AD=7$.

Hint:

A path with less edges has its weight increase less under the add-1-to-each-edge scenario than a path with more edges. So a path with initially higher weight could be surpassed by a lower weight path with more edges.

- Proof of Riemann Hypothesis
- How can we show that an abelian group of order <1024 has a set of generators of cardinality <10
- Sobolev spaces fourier norm equivalence
- Floor function properties: $ = + $ and $ = \sum_{k = 0}^{n – 1} $
- Show that $\sqrt{2+\sqrt{2+\sqrt{2…}}}$ converges to 2
- Evaluate $\int_0^1 \frac{x^k-1}{\ln x}dx $ using high school techniques
- estimate population percentage within an interval, given a small sample
- Lie group, differential of multiplication map
- If n balls are thrown into k bins, what is the probability that every bin gets at least one ball?
- Finding the location of an image of the Mandelbrot set
- Proving Riemann Sums via Analysis
- Example of two norms on same space, non-equivalent, with one dominating the other
- How can I determine the number of wedge products of $1$-forms needed to express a $k$-form as a sum of such?
- Can a neighbourhood of a point be an singleton set?
- Greibach normal form conversion