{"id":160353,"date":"2023-09-26T13:44:21","date_gmt":"2023-09-26T08:14:21","guid":{"rendered":"https:\/\/www.gkseries.com\/blog\/?p=160353"},"modified":"2023-09-26T13:44:22","modified_gmt":"2023-09-26T08:14:22","slug":"consider-the-following-undirected-graph-g","status":"publish","type":"post","link":"https:\/\/www.gkseries.com\/blog\/consider-the-following-undirected-graph-g\/","title":{"rendered":"Consider the following undirected graph G"},"content":{"rendered":"\n<p>Q. Consider the following undirected graph G:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/09\/Screenshot-962.png\" alt=\"\" class=\"wp-image-160354\" style=\"width:245px;height:187px\" width=\"245\" height=\"187\" srcset=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/09\/Screenshot-962.png 336w, https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/09\/Screenshot-962-300x229.png 300w\" sizes=\"(max-width: 245px) 100vw, 245px\" \/><\/figure>\n\n\n\n<p>Choose a value for <em>x <\/em>that will maximize the number of minimum weight spanning trees (MWSTs) of G. The number of MWSTs of G for this value of <em>x <\/em>is<\/p>\n\n\n\n<p>Ans: 4<\/p>\n\n\n\n<p>Sol:<\/p>\n\n\n\n<p>To maximize the number of minimum weight spanning trees of G, the value of x will be 5 because it will have two more choices for corner vertex which will maximize maximum number of MSTs.<\/p>\n\n\n\n<p>Now, according to kruskal algorithm for MST:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Edges with weights 1 and 3 will be selected first,<\/li>\n\n\n\n<li>Now bottom edge with weight 4 will not be selected as will cause cycle on MST,<\/li>\n\n\n\n<li>both corner vertices have two-two choices to select the vertices, so these corner edges with weights 4 and 5 will resultant 2*2 = 4 MSTs.<\/li>\n<\/ol>\n\n\n\n<p>Therefore, total number of MSTs are 2*2 = 4, which is answer.<\/p>\n\n\n\n<p>Note that the value of x is 5, but the number of MWSTs is 4 as shown above.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Q. Consider the following undirected graph G: Choose a value for x that will maximize the number of minimum weight spanning trees (MWSTs) of G. The number of MWSTs of G for this value of x is Ans: 4 Sol: To maximize the number of minimum weight spanning trees of G, the value of x [&hellip;]<\/p>\n","protected":false},"author":419,"featured_media":160355,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[5141],"tags":[5140],"class_list":["post-160353","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\/160353","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=160353"}],"version-history":[{"count":1,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/160353\/revisions"}],"predecessor-version":[{"id":160356,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/160353\/revisions\/160356"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/160355"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=160353"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=160353"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=160353"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}