8387

7768

كارشناسي ارشد

رياضي كاربردي

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1392

هفت،94ص.

ص.ع.به فارسي و انگليسي

رياضي

ID7768

به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي

Orthogonal vector coloring of graphs Fatemeh Modalleliyan f modalleliyan@math iut ac ir September 09 2013 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Behnaz Omoomi bomoomi@cc iut ac ir Advisor Dr Ramin Javadi rjavadi@cc iut ac ir 2010 MSC 05C15 Keywords vector representation orthogonal vector coloring k vector choosable k subspace choosable Abstract Given a eld F subsets S A B and C of F a positive integer d and a nondegeneratebilinear form f x y on Fd a vector representation of a simple graph G with verticesv1 vn is a list of vectors 1 n in Fd whose i is assigned to vertex vi components v v vare in S such that for all i and j f i i A if vi is adjacent to vj in G then f i j B vv vvand if vi is not adjacent to vj in G then f i j C vvThis de nition presented in 1987 by Parsons and Pisanski Then Gerald Haynes and et al in 2008 with choice of A 0 B 0 F C S and f x y as inner product consid ered a special kind of vector representation for graph G and called that orthogonal vectorcoloring of G Accordingly k vector choosable and k subspace choosable graphs thatare vector equivalent of de nition k choosable graphs were introduced These de nitions asfollows For graph G a valid orthogonal k vector coloring over the eld F of G is a vector rep resentation of G with F S C A 0 B 0 and d k The vector chromatic

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رامين جوادي

عباداله محموديان، غلامرضا اميدي