{"id":14511,"date":"2016-02-25T19:06:35","date_gmt":"2016-02-25T19:06:35","guid":{"rendered":"http:\/\/www.oracletutoring.ca\/blog\/?p=14511"},"modified":"2016-02-25T19:06:35","modified_gmt":"2016-02-25T19:06:35","slug":"math-comp-sci-graph-theory-what-is-a-cut-set","status":"publish","type":"post","link":"https:\/\/www.oracletutoring.ca\/blog\/math-comp-sci-graph-theory-what-is-a-cut-set\/","title":{"rendered":"Math & Comp Sci: Graph theory: what is a cut set?"},"content":{"rendered":"

The tutor defines cut set with a couple of examples.<\/h1>\n

When one imagines a cut set, one imagines removing edges from a graph, but not the vertices they connect. <\/p>\n

In this context, we are thinking of undirected graphs. <\/p>\n

A cut set<\/em> is the minimum number of edges whose removal will disconnect a given portion of the graph. Each cut set is specific to a portion of the graph to be disconnected.<\/p>\n

Consider the graph below:<\/p>\n

<\/p>\n

To disconnect just the vertex A from the graph, edges AB and AE need to be removed. The corresponding cut set is {AE, AB}. This may also be written {{A,E},{A,B}}, meaning “[the set containing] the edge from A to E or E to A, and the edge from A to B or B to A”.<\/p>\n

{DP}, or {{D,P}}, is also a cut set: removing the edge DP separates the two cyclic portions of the graph.<\/p>\n

When we disconnect one part of a graph from the rest, we say the number of components of the graph has increased by 1. A graph’s number of components is its number of isolated parts. Before any cut sets are applied, a connected graph (such as the one above) has 1 component: \u03ba(graph)=1. A component, within itself, can be called a connected component<\/em>.<\/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 defines cut set with a couple of examples. When one imagines a cut set, one imagines removing edges from a graph, but not the vertices they connect. In this context, we are thinking of undirected graphs. A cut …<\/p>\n

Math & Comp Sci: Graph theory: what is a cut set?<\/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":[1458,1444,1457],"class_list":["post-14511","post","type-post","status-publish","format-standard","hentry","category-computer-science","category-math","tag-components-of-a-graph","tag-graph-theory","tag-what-is-a-cut-set"],"_links":{"self":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/14511","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=14511"}],"version-history":[{"count":20,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/14511\/revisions"}],"predecessor-version":[{"id":14531,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/14511\/revisions\/14531"}],"wp:attachment":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/media?parent=14511"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/categories?post=14511"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/tags?post=14511"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}