{"id":14575,"date":"2016-03-01T19:18:47","date_gmt":"2016-03-01T19:18:47","guid":{"rendered":"http:\/\/www.oracletutoring.ca\/blog\/?p=14575"},"modified":"2016-03-01T19:18:47","modified_gmt":"2016-03-01T19:18:47","slug":"math-comp-sci-graph-theory-complete-graph","status":"publish","type":"post","link":"https:\/\/www.oracletutoring.ca\/blog\/math-comp-sci-graph-theory-complete-graph\/","title":{"rendered":"Math & Comp Sci: Graph theory: Complete graph"},"content":{"rendered":"

The tutor introduces the idea of the complete graph.<\/h1>\n

The complete graph on n vertices, Kn<\/sub>, means the graph in which each vertex is connected to each other one.<\/p>\n

When two vertices are connected by an edge, they can be called adjacent. Therefore, the complete graph Kn<\/sub> has n vertices, each adjacent to all the others.<\/p>\n

With Kn<\/sub>, the degree of each vertex (meaning the number of other vertices to which it is adjacent) is n-1. The number of edges, |E|, for Kn<\/sub> can be gotten two ways:<\/p>\n

    \n
  1. |E| = nC2. Reason: each edge joins a pair of vertices. Therefore, for Kn<\/sub>, the number of edges is the number of possible pairs of vertices, which is nC2.\n<\/li>\n

    <\/p>\n

  2. \nFor any graph, the sum of the degrees of the vertices is twice the number of edges: ∑deg(v) = 2|E|. Then, for Kn<\/sub>, ∑deg(v)=n(n-1)=2|E|, which means
    n(n-1)\/2 = |E|.\n<\/li>\n<\/ol>\n

    Reassuringly, nC2 = n(n-1)\/2.<\/p>\n

    HTH:)<\/p>\n

    Source:<\/p>\n

    Grimaldi, Ralph P. Discrete and Combinatorial Mathematics<\/u>. Don Mills: Addison-
      Wesley, 1994.<\/p>\n

    Jack of Oracle Tutoring by Jack and Diane,<\/a> Campbell River, BC.<\/p>\n","protected":false},"excerpt":{"rendered":"

    The tutor introduces the idea of the complete graph. The complete graph on n vertices, Kn, means the graph in which each vertex is connected to each other one. When two vertices are connected by an edge, they can be …<\/p>\n

    Math & Comp Sci: Graph theory: Complete graph<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[105,3],"tags":[1470,1471,1467,1444,1469,1468],"class_list":["post-14575","post","type-post","status-publish","format-standard","hentry","category-computer-science","category-math","tag-adjacent-vertices","tag-complete-graph","tag-degree-of-a-vertex","tag-graph-theory","tag-kn","tag-number-of-edges-of-complete-graph"],"_links":{"self":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/14575","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/comments?post=14575"}],"version-history":[{"count":15,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/14575\/revisions"}],"predecessor-version":[{"id":14590,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/14575\/revisions\/14590"}],"wp:attachment":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/media?parent=14575"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/categories?post=14575"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/tags?post=14575"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}