پديد آورنده :
جان نثاري، محسن
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده رياضي
يادداشت :
ص.ع.به فارسي وانگليسي
استاد راهنما :
بهنازعمومي
استاد مشاور :
غلامرضااميدي
توصيفگر ها :
مجموعه هاي كاشف , كدمتريك , پايه متريك , بعدمجاورتي , عددكاشف , گراف تصادفيk-بعدي , گراف باپايه يكتا
تاريخ نمايه سازي :
2/8/91
استاد داور :
عبادالله محموديان،ميثم عليشاهي،جوادباقريان
كد ايرانداك :
ID458 دكتري
چكيده فارسي :
به فارسي وانگليسي:قابل رويت درنسخه ديجيتالي
چكيده انگليسي :
AbstractFor an ordered set W w1 w2 wk of vertices and a vertex v in a connectedgraph G the ordered k vector r v W d v w1 d v w2 d v wk is called the metric representation of v with respect to W where d x y is thedistance between the vertices x and y The set W is called a resolving set for G ifdistinct vertices of G have distinct representations with respect to W A resolvingset for G with minimum cardinality is called a basis of G and its cardinality is themetric dimension of G This concept was introduced in 1975 by slater He describedthe usefulness of these concepts when working with U S Sonar and Coast GuardLoran stations After that it was studied in several papers The concept of a resolving set has various applications in diverse areas includ ing coin weighing problems network discovery and veri cation robot navigation mastermind game problems of pattern recognition and image processing and com binatorial search and optimization This thesis is aimed to study the metric dimension of graphs and open problemsabout it The metric dimension of the cartesian product of graphs was studied in2007 In this thesis the metric dimension of lexicographic is considered Randomlyk dimensional graphs are grphs that every k subset of their vertices forms a metricbasis Properties of these graphs are studied and all randomly k dimensional graphsare characterized Infact randomly k dimensional graphs have the most number ofbases in the other point there are graphs with a unique metric basis The propre rties of these graphs are studied in this thesis In order to characterizing graphswith certain metric dimension all n vertex graphs with metric dimension n 3 arecharacterized Keywords Resolving Sets Metric Representation Metric Dimension Basis Ad jacency Basis Resolving Number Randomly k dimensional
استاد راهنما :
بهنازعمومي
استاد مشاور :
غلامرضااميدي
استاد داور :
عبادالله محموديان،ميثم عليشاهي،جوادباقريان
