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Algebraic Integers as Chromatic and Domination Roots
Joint Authors
Source
International Journal of Combinatorics
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-05-14
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
Let G be a simple graph of order n and λ∈ℕ.
A mapping f:V(G)→{1,2,…,λ} is called a λ-colouring of G if f(u)≠f(v) whenever the vertices u and v are adjacent in G.
The number of distinct λ-colourings of G, denoted by P(G,λ), is called the chromatic polynomial of G.
The domination polynomial of G is the polynomial D(G,λ)=∑i=1nd(G,i)λi, where d(G,i) is the number of dominating sets of G of size i.
Every root of P(G,λ) and D(G,λ) is called the chromatic root and the domination root of G, respectively.
Since chromatic polynomial and domination polynomial are monic polynomial with integer coefficients, its zeros are algebraic integers.
This naturally raises the question: which algebraic integers can occur as zeros of chromatic and domination polynomials? In this paper, we state some properties of this kind of algebraic integers.
American Psychological Association (APA)
Alikhani, Saeid& Hasni, Roslan. 2012. Algebraic Integers as Chromatic and Domination Roots. International Journal of Combinatorics،Vol. 2012, no. 2012, pp.1-8.
https://search.emarefa.net/detail/BIM-497451
Modern Language Association (MLA)
Alikhani, Saeid& Hasni, Roslan. Algebraic Integers as Chromatic and Domination Roots. International Journal of Combinatorics No. 2012 (2012), pp.1-8.
https://search.emarefa.net/detail/BIM-497451
American Medical Association (AMA)
Alikhani, Saeid& Hasni, Roslan. Algebraic Integers as Chromatic and Domination Roots. International Journal of Combinatorics. 2012. Vol. 2012, no. 2012, pp.1-8.
https://search.emarefa.net/detail/BIM-497451
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-497451