Chromatic polynomials and representations of the symmetric group
نویسندگان
چکیده
منابع مشابه
Chromatic Polynomials and Representations of the Symmetric Group
The chromatic polynomial P (G; k) is the function which gives the number of ways of colouring a graph G when k colours are available. The fact that it is a polynomial function of k is essentially a consequence of the fact that, when k exceeds the number of vertices of G, not all the colours can be used. Another quite trivial property of the construction is that the names of the k colours are im...
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In the main this paper introduces the concept of chromatic harmonic polynomials denoted, $H^chi(G,x)$ and chromatic harmonic indices denoted, $H^chi(G)$ of a graph $G$. The new concept is then applied to finding explicit formula for the minimum (maximum) chromatic harmonic polynomials and the minimum (maximum) chromatic harmonic index of certain graphs. It is also applied to split graphs and ce...
متن کاملChromatic polynomials of some nanostars
Let G be a simple graph and (G,) denotes the number of proper vertex colourings of G with at most colours, which is for a fixed graph G , a polynomial in , which is called the chromatic polynomial of G . Using the chromatic polynomial of some specific graphs, we obtain the chromatic polynomials of some nanostars.
متن کاملPfaffians and Representations of the Symmetric Group
Pfaffians of matrices with entries z[i, j]/(xi + xj), or determinants of matrices with entries z[i, j]/(xi−xj), where the antisymmetrical indeterminates z[i, j] satisfy the Plücker relations, can be identified with a trace in an irreducible representation of a product of two symmetric groups. Using Young’s orthogonal bases, one can write explicit expressions of such Pfaffians and determinants, ...
متن کاملSingular polynomials for the symmetric group and Krawtchouk polynomials
A singular polynomial is one which is annihilated by all Dunkl operators for a certain parameter value. These polynomials were first studied by Dunkl, de Jeu and Opdam, (Trans. Amer. Math. Soc. 346 (1994), 237-256). This paper constructs a family of such polynomials associated to the irreducible representation (N − 2, 1, 1) of the symmetric group SN for odd N and parameter values − 1 2 ,− 3 2 ,...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2002
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(01)00610-3