4424

4174

كارشناسي ارشد

رياضي محض

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1387

[هشت]،11،[II]ص.

ص.ع به :فارسي و انگلسي

بهناز عمومي

غلامرضا اميدي

فارسي به انگليسي -انگليسي به فارسي

18/1/88

عبدا.. محموديان ،عاطفه قرباني

1396/09/11

كتابنامه

رياضي

ID4174

به فارسي و انگليسي :قابل رويت در نسخه ديجيتال

On the Total Restrained Domination Number of Graphs Zeinab Maleki zmaleki@math iut ac ir October 15 2008 Master of Science Thesis Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 IranSupervisor Dr Behnaz Omoomi bomoomi@cc iut ac ir Advisor Dr Gholam Reza Omidi romidi@cc iut ac ir Department Graduate Program Coordinator Dr Rasoul Nasr Isfahani isfahani@cc iut ac ir Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran AbstractOne of the important parameters in graph theory in terms of applications and researchattractiveness is domination number A subset D of vertices in graph G V E is calleda dominating set of G if every vertex in V D is adjacent to a vertex in D The conceptof domination in graphs with its many variations are now well studied in graph theory andthere are many articles and books in this regard One of the variations of this parameter istotal restrained domination concept in graphs which is introduced in 2005 by De Xinang Maet al A subset D of vertices in graph G V E is called a total restrained dominatingset of G if D is a dominating set of G and the induced subgraphs D and V D haveno isolated vertex The total restrained domination number of G denoted by tr G is theminimum cardinality of a total restrained dominating set of G As for an application assume that we are selecting a committee from a group of peoplesuch that every nonmember of the committee knows at least one member of the committee each member of the committee has an acquaintance in the committee each nonmember of the committee has an acquaintance out of the committee Obviously the desired committee is corresponding to a total restrained dominating set ofacquaintance graph of the members In this thesis among the studying of the known results in this concept we de ned somenew concepts which help us to provide some new bounds for the total restrained dominationnumber of graphs In this thesis among the many other results we nd a lower bound and an upper boundfor tr as follows Note that G is the minimum size of an edge cover of G Theorem 1 If G is a graph with n vertices and m edges then tr G G n m Theorem 2 If G is a connected graph of order n n 4 and minimum degree 2 then n tr G n 4 4 1

بهناز عمومي

غلامرضا اميدي

عبدا.. محموديان ،عاطفه قرباني