{"id":102,"date":"2020-04-16T03:03:22","date_gmt":"2020-04-16T03:03:22","guid":{"rendered":"http:\/\/blogs.rollins.edu\/graphembeddings\/?page_id=102"},"modified":"2020-05-05T09:52:29","modified_gmt":"2020-05-05T09:52:29","slug":"complete-bipartite-graph-kpp","status":"publish","type":"page","link":"https:\/\/blogs.rollins.edu\/graphembeddings\/embedding-complete-bipartite-graphs-with-cayley-maps\/complete-bipartite-graph-kpp\/","title":{"rendered":"Complete Bipartite Graph Kp,p"},"content":{"rendered":"\n\n\n<div class=\"wp-block-image\"><figure class=\"alignright size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/blogs.rollins.edu\/graphembeddings\/wp-content\/uploads\/2020\/04\/Untitled-1.jpg\" alt=\"\" class=\"wp-image-103\" width=\"67\" height=\"104\" srcset=\"https:\/\/blogs.rollins.edu\/graphembeddings\/wp-content\/uploads\/2020\/04\/Untitled-1.jpg 226w, https:\/\/blogs.rollins.edu\/graphembeddings\/wp-content\/uploads\/2020\/04\/Untitled-1-192x300.jpg 192w\" sizes=\"auto, (max-width: 67px) 100vw, 67px\" \/><figcaption><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/blogs.rollins.edu\/graphembeddings\/wp-content\/ql-cache\/quicklatex.com-abb04cbdb7a51e4fd305d7c8939dab77_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#75;&#95;&#123;&#51;&#44;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"33\" style=\"vertical-align: -6px;\"\/><\/figcaption><\/figure><\/div>\n\n\n\n<p><strong>Complete Bipartite Graphs<\/strong><br>A graph is a complete bipartite graph <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/blogs.rollins.edu\/graphembeddings\/wp-content\/ql-cache\/quicklatex.com-7b4d32354eec1e4b26c0ab379a6e4842_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#75;&#95;&#123;&#110;&#44;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"35\" style=\"vertical-align: -6px;\"\/> if and only if it has <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/blogs.rollins.edu\/graphembeddings\/wp-content\/ql-cache\/quicklatex.com-b0c9da85205ac229dfbcae548384fac4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"20\" style=\"vertical-align: 0px;\"\/> vertices, where the vertices are split into two sets, with <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/blogs.rollins.edu\/graphembeddings\/wp-content\/ql-cache\/quicklatex.com-838e41b97e5ef98519bbe6dc5a884d57_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"\/> vertices in each set. Every vertex of the first set is adjacent to every vertex of the second set, but no vertex is adjacent to another vertex in its same set. <\/p>\n\n\n\n<div style=\"height:20px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Complete Bipartite GraphsA graph is a complete bipartite graph $K_{n,n}$ if and only if it has $2n$ vertices, where the vertices are split into two sets, with $n$ vertices in each set. Every vertex of the first set is adjacent to every vertex of the second set, but no vertex is adjacent to another vertex [&hellip;]<\/p>\n","protected":false},"author":5,"featured_media":0,"parent":97,"menu_order":1,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-102","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/blogs.rollins.edu\/graphembeddings\/wp-json\/wp\/v2\/pages\/102","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.rollins.edu\/graphembeddings\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/blogs.rollins.edu\/graphembeddings\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.rollins.edu\/graphembeddings\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.rollins.edu\/graphembeddings\/wp-json\/wp\/v2\/comments?post=102"}],"version-history":[{"count":29,"href":"https:\/\/blogs.rollins.edu\/graphembeddings\/wp-json\/wp\/v2\/pages\/102\/revisions"}],"predecessor-version":[{"id":417,"href":"https:\/\/blogs.rollins.edu\/graphembeddings\/wp-json\/wp\/v2\/pages\/102\/revisions\/417"}],"up":[{"embeddable":true,"href":"https:\/\/blogs.rollins.edu\/graphembeddings\/wp-json\/wp\/v2\/pages\/97"}],"wp:attachment":[{"href":"https:\/\/blogs.rollins.edu\/graphembeddings\/wp-json\/wp\/v2\/media?parent=102"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}