{"id":154026,"date":"2023-08-02T12:05:08","date_gmt":"2023-08-02T06:35:08","guid":{"rendered":"https:\/\/www.gkseries.com\/blog\/?p=154026"},"modified":"2023-08-02T12:05:11","modified_gmt":"2023-08-02T06:35:11","slug":"let-%f0%9d%90%ba-be-an-undirected-complete-graph-on-%f0%9d%91%9b-vertices-where-%f0%9d%91%9b-2-then-the-number-of-different-hamiltonian-cycles-in-%f0%9d%90%ba-is-equal-to","status":"publish","type":"post","link":"https:\/\/www.gkseries.com\/blog\/let-%f0%9d%90%ba-be-an-undirected-complete-graph-on-%f0%9d%91%9b-vertices-where-%f0%9d%91%9b-2-then-the-number-of-different-hamiltonian-cycles-in-%f0%9d%90%ba-is-equal-to\/","title":{"rendered":"Let \ud835\udc3a be an undirected complete graph on \ud835\udc5b vertices, where \ud835\udc5b > 2. Then, the number of different Hamiltonian cycles in \ud835\udc3a is equal to"},"content":{"rendered":"\n<p>Q. Let \ud835\udc3a be an undirected complete graph on \ud835\udc5b vertices, where \ud835\udc5b > 2. Then, the number of different Hamiltonian cycles in \ud835\udc3a is equal to<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"840\" height=\"71\" src=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/08\/Screenshot-484.png\" alt=\"\" class=\"wp-image-154027\" srcset=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/08\/Screenshot-484.png 840w, https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/08\/Screenshot-484-300x25.png 300w, https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/08\/Screenshot-484-768x65.png 768w\" sizes=\"auto, (max-width: 840px) 100vw, 840px\" \/><\/figure>\n\n\n\n<p>Ans: Option D<\/p>\n\n\n\n<p>Solution:<\/p>\n\n\n\n<p>A simple circuit in a graph G that passes through every vertex exactly once is called a Hamiltonian circuit. In Hamiltonian cycle is a Hamiltonian circuit in which initial and final vertex are same. In an undirected complete graph on n vertices, there are n permutations are possible to visit every node. But from these permutations, there are: n different places (i.e., nodes) you can start; two (clockwise or anticlockwise) different directions you can travel. So, any one of these n! cycles is in a set of 2n cycles which all contain the same set of edges.<\/p>\n\n\n\n<p>So, there are =<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"63\" height=\"34\" src=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/08\/Screenshot-485.png\" alt=\"\" class=\"wp-image-154028\"\/><\/figure>\n\n\n\n<p>distinct Hamilton cycles.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Q. Let \ud835\udc3a be an undirected complete graph on \ud835\udc5b vertices, where \ud835\udc5b > 2. Then, the number of different Hamiltonian cycles in \ud835\udc3a is equal to Ans: Option D Solution: A simple circuit in a graph G that passes through every vertex exactly once is called a Hamiltonian circuit. In Hamiltonian cycle is a [&hellip;]<\/p>\n","protected":false},"author":419,"featured_media":154030,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5141],"tags":[5140],"offerexpiration":[],"class_list":["post-154026","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-gate","tag-gate-questions"],"_links":{"self":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/154026","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/users\/419"}],"replies":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/comments?post=154026"}],"version-history":[{"count":1,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/154026\/revisions"}],"predecessor-version":[{"id":154031,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/154026\/revisions\/154031"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/154030"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=154026"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=154026"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=154026"},{"taxonomy":"offerexpiration","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/offerexpiration?post=154026"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}