Results 1 to 10 of about 567,975 (167)
Realizing string-net condensation: Fibonacci anyon braiding for universal gates and sampling chromatic polynomials [PDF]
Nature CommunicationsThe remarkable complexity of a topologically ordered many-body quantum system is encoded in the characteristics of its anyons. Quintessential predictions emanating from this complexity employ the Fibonacci string net condensate (Fib SNC) and its anyons ...
Zlatko K. Minev +7 more
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New bounds for chromatic polynomials and chromatic roots [PDF]
Discrete Mathematics, 2015 If G is a k -chromatic graph of order n then it is known that the chromatic polynomial of G , π ( G , x ) , is at most x ( x - 1 ) ? ( x - ( k - 1 ) ) x n - k = ( x ) ? k x n - k for every x ? N . We improve here this bound by showing that π ( G , x ) ? (
Jason I Brown, Aysel Erey
exaly +4 more sources
Algorithms for computing chromatic polynomials and chromatic index polynomials
Scientific AfricanObjectives: The aim of this article is to enhance the understanding of the computation of chromatic polynomials and chromatic index polynomials, and to facilitate their practical use in various fields by demonstrating and supporting the proposed ...
Mamo Abebe Ashebo +2 more
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Connection between Graphs' Chromatic and Ehrhart Polynomials [PDF]
Journal of Applied Sciences and Nanotechnology, 2023 Graph Theory is a discipline of mathematics with numerous outstanding issues and applications in a variety of sectors of mathematics and science. The chromatic polynomial is a type of polynomial that has useful and attractive qualities.
Ola Neamah, Shatha Salman
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Problems on chromatic polynomials of hypergraphs
Electronic Journal of Graph Theory and Applications, 2020 Chromatic polynomials of graphs have been studied extensively for around one century. The concept of chromatic polynomial of a hypergraph is a natural extension of chromatic polynomial of a graph. It also has been studied for more than 30 years.
Ruixue Zhang, Fengming Dong
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Application of maple on computing strong fuzzy chromatic polynomial of fuzzy graphs [PDF]
BMC Research Notes, 2022 Objective In the field of graph theory, maple is a technical computation form that is used for solving problems. In this article, we apply maple to find the strong fuzzy chromatic polynomial of fuzzy graphs and related. Moreover, we apply maple to obtain
Mamo Abebe Ashebo +2 more
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Note on chromatic polynomials of the threshold graphs
Electronic Journal of Graph Theory and Applications, 2019 Let G be a threshold graph. In this paper, we give, in first hand, a formula relating the chromatic polynomial of Ḡ (the complement of G) to the chromatic polynomial of G.
Noureddine Chikh, Miloud Mihoubi
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Properties of chromatic polynomials of hypergraphs not held for chromatic polynomials of graphs [PDF]
European Journal of Combinatorics, 2016 In this paper, we present some properties on chromatic polynomials of hypergraphs which do not hold for chromatic polynomials of graphs. We first show that chromatic polynomials of hypergraphs have all integers as their zeros and contain dense real zeros
Ruixue Zhang, F. Dong
semanticscholar +4 more sources
Chromatic Polynomials of Oriented Graphs [PDF]
The Electronic Journal of Combinatorics, 2018 The oriented chromatic polynomial of a oriented graph outputs the number of oriented $k$-colourings for any input $k$. We fully classify those oriented graphs for which the oriented graph has the same chromatic polynomial as the underlying simple graph ...
Danielle Cox, Christopher Duffy
semanticscholar +5 more sources
Measurement of Longitudinal Chromatic Aberration in the Last Crystalline Lens Surface Using Hartmann Test and Purkinje Images [PDF]
Sensors, 2022 Research has shown that longitudinal chromatic aberration (LCA) of the human eye is generated across all of the eye’s optical surfaces. However, it may not be necessary to measure the LCA from the first surface of the cornea to the retina, as it is known
Uriel Calderon-Uribe +2 more
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