{"id":33701,"date":"2020-10-29T21:15:47","date_gmt":"2020-10-29T18:15:47","guid":{"rendered":"http:\/\/ihcoedu.uobaghdad.edu.iq\/?p=33701"},"modified":"2020-11-10T10:43:08","modified_gmt":"2020-11-10T07:43:08","slug":"%d9%82%d8%b3%d9%85-%d8%a7%d9%84%d8%b1%d9%8a%d8%a7%d8%b6%d9%8a%d8%a7%d8%aa-%d9%8a%d9%86%d8%a7%d9%82%d8%b4-%d8%a7%d8%b7%d8%b1%d9%88%d8%ad%d8%a9-%d8%af%d9%83%d8%aa%d9%88%d8%b1%d8%a7%d9%87-%d8%aa%d8%a8-3","status":"publish","type":"post","link":"https:\/\/ihcoedu.uobaghdad.edu.iq\/?p=33701","title":{"rendered":"\u0642\u0633\u0645 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u064a\u0646\u0627\u0642\u0634 \u0627\u0637\u0631\u0648\u062d\u0629 \u062f\u0643\u062a\u0648\u0631\u0627\u0647 \u062a\u0628\u062d\u062b \u0641\u064a \u0647\u064a\u0645\u0646\u0629 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a"},"content":{"rendered":"

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    \n
  • \n

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  • \n

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    \n

    \u00a0\u00a0New Approach in Graph Domination<\/span><\/h3>\n

    By Mohammed Abdali Abdlhusein Sultan<\/span><\/h3>\n

    Supervised by: Prof. Dr. Manal Naji Al-Harere<\/span><\/h3>\n

    \u00a0Abstract<\/span><\/h3>\n

    In this thesis, new ten models of domination in graphs are introduced with several bounds and properties. Pitchfork domination is the main model that is defined and studied here. This type of domination is determined by the number of dominated vertices, which is beneficial for any type of networks that requires such characteristics. In this model, every vertex in the pitchfork dominating set dominates at least j vertices and at most k vertices from the complement set for non-negative integers j and k. In this thesis, every vertex in the pitchfork dominating set, dominates one or two vertices which is studied as a special case. Some bounds on the pitchfork domination number related to the order, size, minimum degree, maximum degree of a graph, and some properties are given. Some new modified graphs are defined in this thesis and their<\/span><\/h3>\n

    pitchfork domination number are evaluated, such as: big helm graph, tadpole flower graph, lollipop flower graph, corresponding barbell graph and barbell-path graph. A question has been answered and discussed that; does every finite, simple and undirected graph without isolated<\/span><\/h3>\n

    vertices have a pitchfork domination or not?. Pitchfork domination number is determined for some standard and complement graphs. Also, for a graphs obtained by join and corona operations. Some upper and lower bounds are proved for different graphs constructed by join operation. Domination problems that implies defining domination vertices by j and k can be solved by this definition, and two sample problems have been presented. Inverse pitchfork domination, the second important model of domination, is studied in this thesis with several results and properties. The inverse pitchfork domination number is evaluated and proved for<\/span><\/h3>\n

    some known graphs. An important conditions are imposed on a vertex to belong to the inverse pitchfork dominating set or not. Independent pitchfork domination model, annihilator pitchfork domination model, doubly connected pitchfork domination model, and total pitchfork domination model are introduced with their inverse models. More bounds, properties and evaluations are given and proved for all these models. Finally, the effects of adding or removing an edge and removing vertex from the graph are studied on the pitchfork domination number<\/span><\/h3>\n

    \u00a0<\/span><\/h4>\n

    <\/h4>\n","protected":false},"excerpt":{"rendered":"

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