Basic terminology, types of graphs, and graph modeling.
Find the number of spanning trees for a complete graph $K_3$.
However, as the chapters progress into vector spaces of graphs, matrix representation (such as incidence and adjacency matrices), and coloring problems, visual intuition fails. The exercises demand a shift toward matrix algebra and boolean operations. Developing solutions for these advanced problems teaches students how to translate a physical, visual network into a system of equations that a computer can process. This specific transition—from picture to matrix to algorithm—is the exact workflow of a modern software engineer or data scientist working on network routing, social media mapping, or logistics. Bridging Theory and Algorithmic Thinking
Exercise 2-1: Show that if a graph has exactly two vertices of odd degree, there must be a path between them.
Question: A connected planar graph has 6 vertices and 10 edges. How many regions does it have? Solution:
Of course, Pokémon Vortex wouldn't be possible without the external help of numerous software developers, digital artists, hosting providers and you, the users.
Here are some of the main thank you's we would like to send out in no particular order.
The Pokémon images you see on the website are courtesy of Xous54. We suggest you follow their work and thank them for providing us with enjoyable digital art to display.
Most generation 6, 7, 8 & 9 sprites are courtesy of Smogon, They are a great source for learning how to battle competitively in the Pokémon games, check them out.
Various generation 6, 7, 8 & 9 sprites are by SpheX, SmartAss & u44151, three talented spriters here on Vortex.
Darkrown is designed by Esepibe and sprited by Rob. We ask that you please don't use it without proper permission. We also suggest you follow Esepibe's work and thank them for the design of Darkrown. Graph Theory By Narsingh Deo Exercise Solution
Most Discord banners used on our server are made from images created by all0412.
Assorted map tiles were made by Kyledove. Follow their work and thank them for making our maps possible.
Custom overworld sprites were made by 874521.
Custom PMD portraits used for profile avatars are courtesy of PMDCollab, and SpheX. Basic terminology, types of graphs, and graph modeling
Font Awesome - Font Awesome is the internet's icon library and toolkit used by millions of designers, developers, and content creators.
jQuery, jQuery UI & jQuery Mobile - jQuery is a fast and compact JavaScript library with immense power to bring HTML to life.
TableSorter - tablesorter.js is a nice, efficient way to integrate the ability of table sorting to your HTML table columns without any hassle.
Bootstrap - Bootstrap is the most popular HTML, CSS, and JS framework for developing responsive, mobile first projects on the web. The exercises demand a shift toward matrix algebra
jStorage - jStorage is a cross-browser key-value store database to store data locally in the browser.
Klass - Klass is an expressive, cross platform JavaScript Class provider with a classical interface to prototypal inheritance.
retina.js - retina.js makes it easy to serve high-resolution images to devices with retina displays.
MediaWiki - MediaWiki is a free software open source wiki package written in PHP - Perfect for compiling a knowledge base on any project.
Basic terminology, types of graphs, and graph modeling.
Find the number of spanning trees for a complete graph $K_3$.
However, as the chapters progress into vector spaces of graphs, matrix representation (such as incidence and adjacency matrices), and coloring problems, visual intuition fails. The exercises demand a shift toward matrix algebra and boolean operations. Developing solutions for these advanced problems teaches students how to translate a physical, visual network into a system of equations that a computer can process. This specific transition—from picture to matrix to algorithm—is the exact workflow of a modern software engineer or data scientist working on network routing, social media mapping, or logistics. Bridging Theory and Algorithmic Thinking
Exercise 2-1: Show that if a graph has exactly two vertices of odd degree, there must be a path between them.
Question: A connected planar graph has 6 vertices and 10 edges. How many regions does it have? Solution:
