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Zbl 1199.05103
Alikhani, Saeid; Peng, Yee-hock
Chromatic zeros and generalized Fibonacci numbers.
(English)
[J] Appl. Anal. Discrete Math. 3, No. 2, 330-335 (2009). ISSN 1452-8630

Let $G$ be a simple graph and $\lambda\in\Bbb N$. A mapping $f: V(G)\to\{1,2,\dots,\lambda\}$ is called a $\lambda$-coloring of $G$ if $f(u)\neq f(v)$, whenever the vertices $u$ and $v$ are adjacent in $G$. The number of distinct $\lambda$-colorings of $G$, denoted by $P(G,\lambda)$ is called chromatic polynomial of $G$. A zero of $P(G,\lambda)$ is called a chromatic zero of $G$. Using a well known fact [{\it B. Jackson}, Combin. Probab. Comput. 2, 325--336 (1993; Zbl 0794.05030)] that $G$ has no chromatic zero in $(-\infty,0)$ the authors prove that neither $2n$-anacci numbers nor their natural powers can be chromatic zeros.
MSC 2000:
*05C15 Chromatic theory of graphs and maps
11B39 Special numbers, etc.
05C31

Keywords: chromatic polynomial; $n$-anacci constants

Citations: Zbl 0794.05030

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