Deprecated: Methods with the same name as their class will not be constructors in a future version of PHP; plgContentJComments has a deprecated constructor in /var/www/astarmathsandphysics/plugins/content/jcomments/jcomments.php on line 25 Call Stack: 0.0001 360736 1. {main}() /var/www/astarmathsandphysics/index.php:0 0.0501 1210872 2. Joomla\CMS\Application\SiteApplication->execute() /var/www/astarmathsandphysics/index.php:49 0.0501 1210872 3. Joomla\CMS\Application\SiteApplication->doExecute() /var/www/astarmathsandphysics/libraries/src/Application/CMSApplication.php:267 0.1345 4131424 4. Joomla\CMS\Application\SiteApplication->dispatch() /var/www/astarmathsandphysics/libraries/src/Application/SiteApplication.php:233 0.1359 4158976 5. Joomla\CMS\Component\ComponentHelper::renderComponent() /var/www/astarmathsandphysics/libraries/src/Application/SiteApplication.php:194 0.1366 4176688 6. Joomla\CMS\Component\ComponentHelper::executeComponent() /var/www/astarmathsandphysics/libraries/src/Component/ComponentHelper.php:356 0.1368 4207208 7. require_once('/var/www/astarmathsandphysics/components/com_content/content.php') /var/www/astarmathsandphysics/libraries/src/Component/ComponentHelper.php:381 0.1379 4229928 8. ContentController->execute() /var/www/astarmathsandphysics/components/com_content/content.php:42 0.1379 4229928 9. ContentController->display() /var/www/astarmathsandphysics/libraries/src/MVC/Controller/BaseController.php:710 0.2089 4899608 10. ContentController->display() /var/www/astarmathsandphysics/components/com_content/controller.php:113 0.2125 5091760 11. Joomla\CMS\Cache\Controller\ViewController->get() /var/www/astarmathsandphysics/libraries/src/MVC/Controller/BaseController.php:663 0.2131 5112688 12. ContentViewArticle->display() /var/www/astarmathsandphysics/libraries/src/Cache/Controller/ViewController.php:102 0.2243 5321872 13. Joomla\CMS\Plugin\PluginHelper::importPlugin() /var/www/astarmathsandphysics/components/com_content/views/article/view.html.php:189 0.2243 5322128 14. Joomla\CMS\Plugin\PluginHelper::import() /var/www/astarmathsandphysics/libraries/src/Plugin/PluginHelper.php:182 Deprecated: Methods with the same name as their class will not be constructors in a future version of PHP; JCommentsACL has a deprecated constructor in /var/www/astarmathsandphysics/components/com_jcomments/classes/acl.php on line 17 Call Stack: 0.0001 360736 1. {main}() /var/www/astarmathsandphysics/index.php:0 0.0501 1210872 2. Joomla\CMS\Application\SiteApplication->execute() /var/www/astarmathsandphysics/index.php:49 0.0501 1210872 3. Joomla\CMS\Application\SiteApplication->doExecute() /var/www/astarmathsandphysics/libraries/src/Application/CMSApplication.php:267 0.1345 4131424 4. Joomla\CMS\Application\SiteApplication->dispatch() /var/www/astarmathsandphysics/libraries/src/Application/SiteApplication.php:233 0.1359 4158976 5. Joomla\CMS\Component\ComponentHelper::renderComponent() /var/www/astarmathsandphysics/libraries/src/Application/SiteApplication.php:194 0.1366 4176688 6. Joomla\CMS\Component\ComponentHelper::executeComponent() /var/www/astarmathsandphysics/libraries/src/Component/ComponentHelper.php:356 0.1368 4207208 7. require_once('/var/www/astarmathsandphysics/components/com_content/content.php') /var/www/astarmathsandphysics/libraries/src/Component/ComponentHelper.php:381 0.1379 4229928 8. ContentController->execute() /var/www/astarmathsandphysics/components/com_content/content.php:42 0.1379 4229928 9. ContentController->display() /var/www/astarmathsandphysics/libraries/src/MVC/Controller/BaseController.php:710 0.2089 4899608 10. ContentController->display() /var/www/astarmathsandphysics/components/com_content/controller.php:113 0.2125 5091760 11. Joomla\CMS\Cache\Controller\ViewController->get() /var/www/astarmathsandphysics/libraries/src/MVC/Controller/BaseController.php:663 0.2131 5112688 12. ContentViewArticle->display() /var/www/astarmathsandphysics/libraries/src/Cache/Controller/ViewController.php:102 0.3773 13738440 13. JEventDispatcher->trigger() /var/www/astarmathsandphysics/components/com_content/views/article/view.html.php:199 0.3776 13738840 14. plgContentJComments->update() /var/www/astarmathsandphysics/libraries/joomla/event/dispatcher.php:160 0.3776 13738840 15. plgContentJComments->onContentAfterDisplay() /var/www/astarmathsandphysics/libraries/joomla/event/event.php:70 0.3778 13747088 16. plgContentJComments->onAfterDisplayContent() /var/www/astarmathsandphysics/plugins/content/jcomments/jcomments.php:339 0.3780 13748824 17. JComments::show() /var/www/astarmathsandphysics/plugins/content/jcomments/jcomments.php:282 0.3786 13781872 18. JCommentsFactory::getACL() /var/www/astarmathsandphysics/components/com_jcomments/jcomments.php:188 0.3787 13782272 19. spl_autoload_call() /var/www/astarmathsandphysics/components/com_jcomments/classes/factory.php:274 0.3787 13782352 20. JLoader::load() /var/www/astarmathsandphysics/components/com_jcomments/classes/factory.php:274

Eulerian From Non Eulerian Graphs

Any network containing odd nodes is non – Eulerian. This means every arc cannot be traced just once, returning to the starting point and returning to the start point. Such a route, from a point traversing every arc once and returning to the start point, is called an Eulerian path.

A network containing odd arcs is non – Eulerian because each node must be entered and exited from separate arcs, so that the number of arcs connected to a node is twice the number of exits or entrances to that arc in traversing the network.

If a network is non Eulerian, we can modify it so that it becomes Eulerian by simply replicating each arc. Each node then becomes even and the network becomes Eulerian.

An attempt to construct an Eulerian path for the network on the left may start DCABCD. The path AD has not been traversed, and if it is there is no way to return to D without travelling over at least one path at least one, since every path has been traversed.

The network on the right has Eulerian path DCABCABCDAD.

Add comment

Security code
Refresh