Results 121 to 130 of about 2,394 (219)

Set maps, umbral calculus, and the chromatic polynomial

, 2005
Some important properties of the chromatic polynomial also hold for any polynomial set map satisfying p_S(x+y)=\sum_{T\uplus U=S}p_T(x)p_U(y). Using umbral calculus, we give a formula for the expansion of such a set map in terms of any ...
Wiseman, Gus
core  

A generalization of chromatic polynomial of a graph subdivision

Considering the partitions of a set into nonempty subsets, we obtain an expression for the number of all partitions of a given type. The chromatic polynomial of a graph subdivision is generalized, considering two sets of colors, and a general explicit ...
Szymanski, J., Cardoso, D. M., Silva, M. E.   +2 more
core   +1 more source

Development of a Python Program for the Calculation of Chromatic Polynomial

, 2021
The chromatic polynomial is a polynomial in a single variable, associated with a graph, that expresses the number of different ways a graph can be properly colored given the number of specified colors. We give the definitions for the vertex coloring of a
Khalid, Asad Ullah
core  

An Exploration of the Chromatic Polynomial

, 2017
In 1912, George Birkhoff was studying the Four Color Problem, and in doing so introduced the concept of the chromatic polynomial. While this did not end up directly contributing to proving that every map could be colored with four colors such that no ...
Aydelotte, Amanda
core  

Polynomials related to chromatic polynomials

, 2020
For a simple graph $G$, let $χ(G,x)$ denote the chromatic polynomial of $G$. This manuscript introduces some polynomials which are related to chromatic polynomial and their relations.
openaire   +2 more sources

A new method for calculating the chromatic polynomial

, 2017
Chromatic polynomials are widely used in graph theoretical or chemical applications in many areas. Birkhoff-Lewis theorem is the most important tool to find the chromatic polynomial of any given graph.
Naci Cangül, İsmail Naci, Sanlı, Utkum   +1 more
core  

تصمیم حاسوبي لعدسة كھروستاتیكیة ثلاثیة الأقطاب

مجلة كلية التربية للبنات, 2019
A low aberration electrostatic lens of three electrode was design, The electrode shapes were determined using solution of Laplace equation . A new Computational technique were used to design an electrostatic lens which depends on the determination ...
أ.د.سمیر خضر العاني ندى عبد الفتاح محمد
doaj  

Balancing chromatic effects in fourth-generation synchrotrons using the quasi-invariants of motion chromatic index

Results in Physics
Fourth-generation synchrotron light sources generate highly brilliant and coherent electromagnetic radiation, valuable in multiple scientific areas.
Edgar Andrés Sánchez, Alain Flores, Jorge Hernández-Cobos, Matías Moreno, Armando Antillón   +4 more
doaj   +1 more source

On the Degree-Chromatic Polynomial of a Tree

, 2017
The degree chromatic polynomial Pm(G,k) of a graph G counts the number of k-colorings in which no vertex has m adjacent vertices of its same color. We prove Humpert and Martin\u27s conjecture on the leading terms of the degree chromatic polynomial of a
Cifuentes, Diego
core  

Chromatic Polynomial of Smarandache Ve-Product of Graph

, 2009
In this paper we determine the chromatic polynomial in the case of the Cartesian and strong product of a tree and a complete ...
Khalil Paryab, Ebrahim Zare
core   +1 more source