What is a King's graph? This video will explain what a King's graph is and how to construct one. <br /><br />A king's graph is a graph that represents all legal moves of a king on a chessboard. Each vertex of a king's graph represents a square on a chessboard, and the edges represent all possible legal moves a king can make between 2 squares on a chessboard. King's graphs can correspond to a chessboard of any size, not just the typical 8 x 8 chessboard. <br /><br />Why are King's graphs interesting? I think they're interesting because we can define them solely using the strong product of two path graphs. It's pretty cool that this actually gives us a graph that captures the properties of the legal moves of a king on a chessboard. I suggest you check out my video on strong products of graphs to review this graph operation featured in this video. <br /><br /><br />Links for more information:<br /><a href="https://en.wikipedia.org/wiki/King%27s_graph" target="_blank" rel="nofollow">https://en.wikipedia.org/wiki/King%27s_graph</a><br /><br /><a href="https://mathworld.wolfram.com/KingGraph.html" target="_blank" rel="nofollow">https://mathworld.wolfram.com/KingGraph.html</a><br /><br /><a href="https://en.wikipedia.org/wiki/Strong_product_of_graphs" target="_blank" rel="nofollow">https://en.wikipedia.org/wiki/Strong_product_of_graphs</a><br /><br />Thanks for watching! If you liked this video, I suggest you check out my other videos in the graph theory playlist: <a href="https://www.youtube.com/playlist?list=PLZ2xtht8y2-Jx8hxFvnFQfEej1PzqFbVX" target="_blank" rel="nofollow">https://www.youtube.com/playlist?list=PLZ2xtht8y2-Jx8hxFvnFQfEej1PzqFbVX</a> <br /><br />Discord: <a href="https://discord.gg/dvpXxBy" target="_blank" rel="nofollow">https://discord.gg/dvpXxBy</a><br />Reddit: <a href="https://www.reddit.com/r/Vitalsine/" target="_blank" rel="nofollow">https://www.reddit.com/r/Vitalsine/</a><br />...<br /><a href="https://www.youtube.com/watch?v=H22Bt1n57Gc" target="_blank" rel="nofollow">https://www.youtube.com/watch?v=H22Bt1n57Gc</a>