Perfect 3-colorings of Heawood graph | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 55، دوره 12، شماره 1، مرداد 2021، صفحه 713-717 اصل مقاله (129.86 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/IJNAA.2021.4901 | ||
| نویسنده | ||
| Mehdi Alaeiyan | ||
| School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16846, Iran | ||
| چکیده | ||
| Perfect coloring is a generalization of the notion of completely regular codes, given by Delsarte. A perfect m-coloring of a graph G with m colors is a partition of the vertex set of G into m parts $A_1, . . . , A_m$ such that, for all $i, j \in \{1, . . . , m\}$, every vertex of $A_i$ is adjacent to the same number of vertices, namely, $a_{ij}$ vertices, of $A_j$. The matrix $A = (a_{ij} )$, $i, j \in \{1, 2,... , m\}$, is called the parameter matrix. We study the perfect 3-colorings (also known as the equitable partitions into three parts) of the Heawood graph. In particular, we classify all the realizable parameter matrices of perfect 3-colorings for the Haywood graphs. | ||
| کلیدواژهها | ||
| perfect coloring؛ parameter matrices؛ cubic graph | ||
| مراجع | ||
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