7273

6779

كارشناسي ارشد

رياضي كاربردي

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1391

هفت، 75ص.: مصور، جدول، نمودار

ص.ع. به فارسي و انگليسي

1396/09/21

كتابنامه

علوم رياضي

رياضي

ID6779

به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي

Vertex Coloring Edge Weighting of Graphs Akbar Davoodi a davoodi@math iut ac ir September 09 2012 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Behnaz Omoomi bomoomi@cc iut ac ir Advisor Dr Gholam Reza Omidi romidi@cc iut ac ir 2010 MSC 05C15 Keywords weighted graph vertex coloring edge weighting AbstractA k total weighting of a simple graph G is a function w E G V G 1 k Atotal weighting is a vertex coloring if for every edge uv E G c u c v where for every vertex v V G c v w v e v w e If such a function w exists then we say thatG admits a vertex coloring k total weighting VCk TW The smallest k for which G admitsa VCk TW is denoted by G This concept was introduced by Przyby o et al DMTCS Vol 12 No 1 pp 101 108 2010 they proposed the conjecture that for every simplegraph G G 2 This conjecture is known as 1 2 conjecture So far the existence of aVC2 TW has been shown for complete graphs 3 colorable graphs 3 regular graphs 4 regulargraphs and graphs of maximum degree 3 It has been recently shown by Kalkowski etal J Combin Theory Ser B Vol 100 No 3 pp 347 349 2010 that every graph has aVC3 TW A k edge weighting of a graph G is a function w E G 1 k An edge weighting naturally induces a vertex coloring c where for every vertex v V G c v e v w e If

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غلامرضا اميدي

عباداله محموديان، رامين جوادي