Ultimate chromatic polynomials
نویسندگان
چکیده
منابع مشابه
Ultimate chromatic polynomials
We outline an approach to enumeration problems which relies on the algebra of free abelian groups, giving as our main application a generalisa-tion of the chromatic polynomial of a simple graph G. Our polynomial lies in the free abelian group generated by the poset K(G) of contractions of G, and reduces to the classical case after a simple substitution. Its main properties may be stated in term...
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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.
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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...
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Table of contents Introduction 1. Relation of the present work to previous researches on map-coloring and summary of results. 356 2. Definitions. 358 Chapter I. First principles in the numerical and theoretical treatment of chromatic polynomials 1. The three fundamental principles. 362 2. The quadrilateral reduction formula. 363 3. The pentagon reduction formula. 365 4. The m-gon reduction form...
متن کاملchromatic polynomials of some nanostars
let g be a simple graph and (g,) denotes the number of proper vertex colourings of gwith at most colours, which is for a fixed graph g , a polynomial in , which is called thechromatic polynomial of g . using the chromatic polynomial of some specific graphs, weobtain the chromatic polynomials of some nanostars.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1994
ISSN: 0012-365X
DOI: 10.1016/0012-365x(94)90174-0