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# The b-chromatic number of power graphs

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## The b-chromatic number of some powergraphs

### Brice Effantin 1 and Hamamache Kheddouci 2

LE2I FRE-CNRS 2309, Universit´e de Bourgogne, B.P. 47870, 21078 Dijon Cedex, France

1brice.effantin@u-bourgogne.fr

2kheddouc@u-bourgogne.fr

1,v2, . . . ,vn

ik,

i

### adjacent to a vertex of every color j, 1

j6=ik. In this paper, we give the exact

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### The study of distance graphs was initiated by Eggleton and al. [4]. Recently, the problem of coloring of this class of graphs has attracted considerable attention, see e.g. [12, 13]. Circulant graphs have been extensively studied and have a vast number of applications to multicomputer networks and distributed computation (see [1, 10]). The special cases we consider are the distance graph G(D) with finite distance set D = {1, 2, . . . , p}which is isomorphic to the p-th power graph of a path and the circulant graph G(n,S)with S = {1, 2, . . . , p}which is isomorphic to the p-th power graph of a cycle.

1365–8050 c2003 Discrete Mathematics and Theoretical Computer Science (DMTCS), Nancy, France

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(4)

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(5)

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(6)

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### .

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(7)

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(8)

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(9)

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(10)

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163

(11)

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### 195-206.

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