Original Research Article

Article volume = 2021 and issue = 2

Pages: 136–142

Article publication Date: November, 1, 2021

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# Perfect 3-Colorings of Some Generalized Peterson Graph

#### Mehdi Alaeiyan, Zahra Shokoohi

School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16846, Iran.

##### Abstract:

The notion of a perfect coloring, introduced by Delsarte, generalizes the concept of completely regular code. A perfect z-colorings of a graph is a partition of its vertex set. It splits vertices into z parts P1, , Pz such that for all i, j 2 f1, , zg, each vertex of Pi is adjacent to pij, vertices of Pj. The matrix P = (pij)i,j2f1, ,zg, is called parameter matrix. In this article, we classify all the realizable parameter matrices of perfect 3-colorings of some the generalized peterson graph.

##### Keywords:

Parameter matrices, Perfect coloring, Equitable partition, Generalized peterson graph.

##### References:

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##### Cite this article as:

- Mehdi Alaeiyan, Zahra Shokoohi, Perfect 3-Colorings of Some Generalized Peterson Graph, Communications in Combinatorics, Cryptography & Computer Science, 2021(2), PP.136–142, 2021
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