منابع مشابه
The Coloring Ideal and Coloring Complex of a Graph
Let G be a simple graph on d vertices. We define a monomial ideal K in the Stanley-Reisner ring A of the order complex of the Boolean algebra on d atoms. The monomials in K are in one-to-one correspondence with the proper colorings of G. In particular, the Hilbert polynomial of K equals the chromatic polynomial of G. The ideal K is generated by square-free monomials, so A/K is the Stanley-Reisn...
متن کاملAssociative graph products and their independence, domination and coloring numbers
Associative products are defined using a scheme of Imrich & Izbicki [18]. These include the Cartesian, categorical, strong and lexicographic products, as well as others. We examine which product ⊗ and parameter p pairs are multiplicative, that is, p(G ⊗ H) ≥ p(G)p(H) for all graphs G and H or p(G⊗H) ≤ p(G)p(H) for all graphs G and H. The parameters are related to independence, domination and ir...
متن کاملComplex Numbers and Exponentials
respectively. It is conventional to use the notation x+iy (or in electrical engineering country x+jy) to stand for the complex number (x, y). In other words, it is conventional to write x in place of (x, 0) and i in place of (0, 1). In this notation, the sum and product of two complex numbers z1 = x1 + iy1 and z2 = x2 + iy2 is given by z1 + z2 = (x1 + x2) + i(y1 + y2) z1z2 = x1x2 − y1y2 + i(x1y...
متن کاملComplex Numbers and Exponentials
respectively. It is conventional to use the notation x+iy (or in electrical engineering country x+jy) to stand for the complex number (x, y). In other words, it is conventional to write x in place of (x, 0) and i in place of (0, 1). In this notation, the sum and product of two complex numbers z1 = x1 + iy1 and z2 = x2 + iy2 is given by z1 + z2 = (x1 + x2) + i(y1 + y2) z1z2 = x1x2 − y1y2 + i(x1y...
متن کاملComplex Numbers and Exponentials
A complex number is nothing more than a point in the xy–plane. The first component, x, of the complex number (x, y) is called its real part and the second component, y, is called its imaginary part, even though there is nothing imaginary about it. The sum and product of two complex numbers (x1, y1) and (x2, y2) are defined by (x1, y1) + (x2, y2) = (x1 + x2, y1 + y2) (x1, y1) (x2, y2) = (x1x2 − ...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2008
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2008.02.033