12049

982 دكتري

دكتري

رياضي

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1395

[هشت]،[86]ص.: مصور، جدول، نمودار

ص. ع. به فارسي و انگليسي

بهناز عمومي، رامين جوادي

غلامرضا اميدي

عباداله محموديان، محرم نژاد ايرد موسي، ميثم عليشاهي

1395/11/10

كتابنامه

علوم رياضي

رياضي

ID982 دكتري

Clique Coverings and Clique Partitions of Graphs Akbar Davoodi akbar davoodi@math iut ac ir September 14 2016 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Behnaz Omoomi bomoomi@cc iut ac ir Supervisor Dr Ramin Javadi rjavadi@cc iut ac ir Advisor Dr Gholam Reza Omidi romidi@cc iut ac ir 2010 MSC 05C70 05C62 05D05 05B05 Keywords clique cover clique partition sigma clique covering edge clique cover sum sigma clique partition local clique covering pairwise balanced design Nordhaus Gadduminequality AbstractLet G be a simple graph A family of cliques of G is called an edge clique covering for G ifevery edge of G belongs to at least one member of the family A clique covering in which eachedge belongs to exactly one clique is called a clique partition The minimum size of a cliquecovering of G is called the clique cover number of G and is denoted by cc G Similarly theclique partition number of G denoted by cp G is de ned as the minimum number of cliquesin a clique partition of G The subject of clique covering has been widely studied in recent decades First time Erd s et al in 9 presented a close relationship between the clique covering and the setintersection representation Also they proved that the clique partition number of a graph onn vertices cannot exceed n2 4 known as Erd s Goodman P sa theorem The connections

بهناز عمومي، رامين جوادي

غلامرضا اميدي

عباداله محموديان، محرم نژاد ايرد موسي، ميثم عليشاهي