%0 Journal Article
%T Algebraic Integers as Chromatic and Domination Roots
%A Saeid Alikhani
%A Roslan Hasni
%J International Journal of Combinatorics
%D 2012
%I Hindawi Publishing Corporation
%R 10.1155/2012/780765
%X Let  be a simple graph of order  and ¡Ê£¿. A mapping ¡Ã()¡ú{1,2,¡­,} is called a -colouring of  if ()¡Ù() whenever the vertices  and  are adjacent in . The number of distinct -colourings of , denoted by (,), is called the chromatic polynomial of . The domination polynomial of  is the polynomial ¡Æ(,)==1(,), where (,) is the number of dominating sets of  of size . Every root of (,) and (,) is called the chromatic root and the domination root of , respectively. Since chromatic polynomial and domination polynomial are monic polynomial with integer coefficients, its zeros are algebraic integers. This naturally raises the question: which algebraic integers can occur as zeros of chromatic and domination polynomials? In this paper, we state some properties of this kind of algebraic integers.
%U http://www.hindawi.com/journals/ijct/2012/780765/