Number of ways painting graph in two colors, such that two nodes of same color are linked by edge

We are given undirected graph of $ N$ nodes and $ M$ edges, we want to count the number of possible ways to paint this graph in $ 2$ colors such that for each two nodes having the same color, there must be an edge between them.

I tried some examples on paper and I always got numbers of the form $ 2^x$ , however I couldn’t see a valid way to find such $ x$ or I couldn’t prove why this is the case.

Does this problem become easier if we are given directed acyclic graph instead of undirected one?

Magento 2 remove version number impact

I noticed if we type /magento_version along with site url then it displays our magento version. So anyone with bad intention can check my version and exploit it.

to prevent this I can disable the magento_version module from command line but not sure disabling this module will impact on any other feature. In code I noticed they are only using controller to display the info. But i am not sure it’s used elsewhere or not. Also, possible magento use it for API or something or for composer based upgrades?

Will there be any negative impact if we disable? Should i hide my version number publicly? Is it good to hide it?

Any help would be appreciated.

Is the control bus “measured” in the number of bits it have?

In the system bus, the data bus and the address bus are “measured” in the number of bits that they have, for example we may say that the data bus is 32-bit and the address bus is 32-bit for some CPU model.

But do we “measure” the control bus in the same way, for example do we say that the control bus is 32-bit for some CPU model, or is the control bus a special case?

Is it possible to intercept messages from email address or phone number that is expired? if yes, how?

I used to have an email account for receiving important messages but it was deleted by the email provider in which they claimed that deletion of the email address is still in progess but cannot be reversed. I desperately need that email address to receive important messages bascially i wonder if its still possible to intercept messages that were sent to the email address If yes, how? Also does this work on phone number as well? is it possible to intercept SMS that is sent to phone numbers in which {the phone number) is no longer in service?

In other words—if someone send a message to that email address/phone number, is it possible to intercept that message before it reached the email address/phone number? If yes, how?

Algorithm for dividing a range into ranges and then finding which range a number belongs to


  • a minimum
  • a maximum
  • number of ranges
  • a value between minimum and maximum

I’m trying to come up with a method, or two, which would calculate which range the provided value belongs to.

For min=1, max = 10, number of ranges=5 the ranges would be [1,2],[3,4],[5,6],[7,8],[9-10]

The other method would behave like shown below:

  • method(1)->[1-2]
  • method(2)->[1-2]
  • method(3)->[3-4]
  • method(4)->[3-4]
  • method(5)->[5-6]
  • method(6)->[5-6]
  • method(7)->[7-8]
  • method(8)->[7-8]
  • method(9)->[9-10]
  • method(10)->[9-10]

This would be used for generating a legend for a map where the size of the marker depends on the range a value belongs to.

I wonder if there is a nice algorithmic solution for this.

The numbers I work with are integers.


Another example:

For min=1, max = 3, number of ranges=2 the ranges would be

a) [1-2],[3-3]


b) [1-1],[2-3]

The other method would behave like shown below:


  • method(1)->[1-2]
  • method(2)->[1-2]
  • method(3)->[3-3]

or b)

  • method(1)->[1-1]
  • method(2)->[2-3]
  • method(3)->[2-3]

I don’t have a preference for a) or b).

incremental number at text string for use in calculated column

I need to create a unique ID number of each new project in the follow format 00-0000-000000 where the middle four digits are a number that increments by one for each new project. I have a list called variables with a column called proj_number which holds a single entry which is incremented by workflow each time a new project site is requested. Here is my issue:

In order to increment the number it must be a number field which has compulsory formatting and won’t stay in a four digit (0000) format so I need either

  1. A way to increment a four digit string by 1 using a work flow or
  2. A way of adding 00s to the number column so that is always four digits long.

any thoughts gratefully received.