9975

9205

كارشناسي ارشد

رياضي كاربردي

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1393

نه، 61ص.: مصور

ص.ع. به فارسي و انگليسي

رامين جوادي

بهناز عمومي

دارد

94/2/16

غلامرضا اميري، محمدرضا عبودي

1396/09/27

كتابنامه

علوم رياضي

رياضي

ID9205

The Sigma Coloring of Graphs Mahdi Jeznabadi m jeznabadi@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 Behnaz Omoomi bomoomi@cc iut ac ir 2010 MSC 05C15 Keywords Neighbor distinguishing coloring Sigma coloring The sigma range AbstractIn this thesis we investigate sigma coloring of graphs and its corresponding parameters For a nontrivial connected graph G let c V G N be a vertex coloring of G where adjacentvertices may be colored the same For a vertex v of G let N v denote the set of vertices adjacent tov The color sum v of v is the sum of the colors of the vertices in N v If u v for everytwo adjacent vertices u and v of G then c is called a sigma coloring of G The minimum number ofcolors required in a sigma coloring of a graph G is called its sigma chromatic number G The sigma chromatic number of a graph G never exceeds its chromatic number G and for everypair a b of positive integers with a b there exists a connected graph G with G a and G b There is a connected graph G of order n with G k for every pair k n of positive integers withk n if and only if k n 1 n 1 For integers n 2 let f n 1 which then is the number of distinct n element multisubsetsof N 1 2 Now for positive integers k and n the sigma chromatic number of the regular complete k partite graph Kk n is the unique positive integer for which f 1 n k f n Let G Kk1 n1 k2 n2 kt nt where n1 n2 nt are t distinct positive integers Then G max Kki ni 1 i t A sigma k coloring of a graph G is an assignment of positive integers 1 2 k to the vertices of Gsuch that for every two adjacent vertices the sums of numbers assigned to their neighbors are di erent The minimum number k for which there exists a sigma k coloring of G is called the sigma range ofG and is denoted by G It is proved that G 468 for every planar graph G This improves

رامين جوادي

بهناز عمومي

غلامرضا اميري، محمدرضا عبودي