{"id":425,"date":"2017-11-06T09:58:09","date_gmt":"2017-11-06T09:58:09","guid":{"rendered":"https:\/\/science.sjp.ac.lk\/mat\/?page_id=425"},"modified":"2017-11-07T03:21:07","modified_gmt":"2017-11-07T03:21:07","slug":"graph-theory","status":"publish","type":"page","link":"https:\/\/science.sjp.ac.lk\/mat\/graph-theory\/","title":{"rendered":"Graph Theory"},"content":{"rendered":"<p><strong>Course: <\/strong>MAT 353 3.0 Graph Theory (Compulsory)<\/p>\n<p style=\"text-align: justify\"><strong>Course content:\u00a0<\/strong><strong>Graphs: <\/strong>Basic Definitions in Graph Theory, Traveling Through a Graph, Connectedness, Euler Tours\u2028, Hamiltonian Cycles, Graph Representation, Adjacency Matrices, Adjacency Lists, Planarity of Graphs, Euler\u2019s Formula\u2028, Kuratowski\u2019s Theorem, Coloring of Graphs, Vertex Coloring, Edge Coloring, Face Coloring and Chromatic Number, Color Theorems; <strong>Trees:<\/strong> Basic Definitions for Trees, Rooted Trees\u2028, Ordered Trees, Binary Trees and m-ary Trees, Spanning Trees, Depth First Search, Breadth First Search, Minimum Spanning Trees, Prim\u2019s Algorithm, Kruskal\u2019s Algorithm, <strong>Paths and Flows<\/strong>: Shortest Paths and Longest Paths, Dijkstra\u2019s Algorithm\u2028, Single-source(sink) Shortest Paths, Multiple-source(Sink) Shortest Paths, Flows, The Ford-Fulkerson Algorithm, The Maxflow-Mincut Theorem, <strong>Matching<\/strong>: Matching and Covers, Maximum Matching\u2028, Hall\u2019s Matching Condition, Min-Max Theorem\u2028, Independent Sets and Covers, Dominating Sets, Algorithms and Applications, Maximum Bipartite Matching, Weighted Bipartite Matching, Stable Matching<\/p>\n<p><strong>Recommended Readings:<\/strong><\/p>\n<p><em>Graph Theory and Its Applications by Jonathan L. Gross and Jay Yellon<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Course: MAT 353 3.0 Graph Theory (Compulsory) Course content:\u00a0Graphs: Basic Definitions in Graph Theory, Traveling Through a Graph, Connectedness, Euler Tours\u2028, Hamiltonian Cycles, Graph Representation, Adjacency Matrices, Adjacency Lists, Planarity of Graphs, Euler\u2019s Formula\u2028, Kuratowski\u2019s Theorem, Coloring of Graphs, Vertex Coloring, Edge Coloring, Face Coloring and Chromatic Number, Color Theorems; Trees: Basic Definitions for Trees, &hellip; <a href=\"https:\/\/science.sjp.ac.lk\/mat\/graph-theory\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Graph Theory<\/span><\/a><\/p>\n","protected":false},"author":4,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_ti_tpc_template_sync":false,"_ti_tpc_template_id":"","footnotes":""},"_links":{"self":[{"href":"https:\/\/science.sjp.ac.lk\/mat\/wp-json\/wp\/v2\/pages\/425"}],"collection":[{"href":"https:\/\/science.sjp.ac.lk\/mat\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/science.sjp.ac.lk\/mat\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/science.sjp.ac.lk\/mat\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/science.sjp.ac.lk\/mat\/wp-json\/wp\/v2\/comments?post=425"}],"version-history":[{"count":2,"href":"https:\/\/science.sjp.ac.lk\/mat\/wp-json\/wp\/v2\/pages\/425\/revisions"}],"predecessor-version":[{"id":487,"href":"https:\/\/science.sjp.ac.lk\/mat\/wp-json\/wp\/v2\/pages\/425\/revisions\/487"}],"wp:attachment":[{"href":"https:\/\/science.sjp.ac.lk\/mat\/wp-json\/wp\/v2\/media?parent=425"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}