پديد آورنده :
جوربنيان، سعيد
عنوان :
گراف هاي تمام نقره اي
مقطع تحصيلي :
كارشناسي ارشد
گرايش تحصيلي :
علوم رياضي - رياضي كاربردي
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
يادداشت :
ص.ع.به فارسي و انگليسي
استاد راهنما :
رامين جوادي
استاد مشاور :
غلامرضا اميدي
توصيفگر ها :
رنگ آميزي گراف ها , رنگ آميزي تمام نقره اي , ماتريس و مكعب نقره اي
تاريخ نمايه سازي :
17/9/93
استاد داور :
بهناز عمومي، محمدرضا عبودي
چكيده انگليسي :
Totally Silver Graphs Saeed Jorbonyan s jorbonyan@math iut ac ir 2014 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Ramin Javadi rjavadi@cc iut ac ir Advisor Dr Gholam Reza Omidi romidi@cc iut ac ir 2010 MSC 05C15 Keywords totally silver coloring totally silver graphs silver matrix silver cube AbstractGraph coloring is an important concept in graph theory A totally silver coloring of a graph G is ak coloring of G such that for every vertex v V G each color appears exactly once in N v theclosed neighborhood of v A totally silver graph is a graph which admits a totally silver coloring Totally silver coloring are directly related to other areas of graph theory such as distance coloring anddomination In this thesis we present several constructive characterizations of totally silver graphsand give several in nite families of these graphs In particular we show that in a totally silver coloringof an r regular graph G all color classes have equal size and V G is a multiple of r 1 Also theorder of every r regular bipartite totally silver graph is a multiple of 2r 2 We also investigate properties of cubic totally silver graphs In particular we show that thegeneralized Petersen graph P n d is totally silver if and only if 4 n and d is odd Also for all n 4 there exists a nontrivial cubic totally silver graph of order 4n Moreover we show that every cubictotally silver graph which is 2 connected or its girth is at most 5 can be reduced to a totally silvergraph of smaller size Then we prove that there exists cubic totally silver graphs whose girth is k for6 k 10 We also introduce the silver matrix and silver cube and examine their properties A silver matrixis an n n matrix whose entries are in S 1 2 2n 1 and for every 1 i n entries of ithrow and ith column containes all numbers in S We prove there is no silver matrix of odd order andsilver matrices of order n exist for every even number n More generally for positive integers n d a dsilver n d cube is a triple Kn I c where I is a maximum independent set in a Cartesian power of
استاد راهنما :
رامين جوادي
استاد مشاور :
غلامرضا اميدي
استاد داور :
بهناز عمومي، محمدرضا عبودي
