منابع مشابه
A Matrix Method for Chromatic Polynomials -ii 1. Introduction
The subject of this paper is the calculation of the chromatic polynomials of families of graphs that have cyclic symmetry. Generally speaking, there are no elegant methods in this eld. The standard method of deletion-and-contraction is both ineecient and inelegant: it requires exponentially many steps, and any symmetry that the graph possesses is destroyed at the very rst step. In this paper we...
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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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A method for calculating flow polynomials based on a transfer matrix is described. It is analogous to the method used for chromatic polynomials, although there is as yet no parallel development of the theory. The new method is applied to a family of bracelets, and the limit curves for the flow roots are obtained. There is an unexplained similarity between these calculations and the correspondin...
متن کاملChromatic Polynomials
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...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2001
ISSN: 0095-8956
DOI: 10.1006/jctb.2000.2017