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Chromatic and clique numbers of a class of perfect graphs | ||
Transactions on Combinatorics | ||
مقاله 1، دوره 4، شماره 4، اسفند 2015، صفحه 1-4 اصل مقاله (197.32 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22108/toc.2015.7340 | ||
نویسنده | ||
Mohammad Reza Fander* | ||
Azad University, Chaluse Branch | ||
چکیده | ||
Let $p$ be a prime number and $n$ be a positive integer. The graph $G_p(n)$ is a graph with vertex set $[n]=\{1, 2,\ldots, n\}$, in which there is an arc from $u$ to $v$ if and only if $u\neq v$ and $p\nmid u+v$. In this paper it is shown that $G_p(n)$ is a perfect graph. In addition, an explicit formula for the chromatic number of such graph is given. | ||
کلیدواژهها | ||
perfect graph؛ Clique number؛ chromatic number | ||
مراجع | ||
R. Diestel (2010) Graph theory Fourth edition, Graduate Texts in Mathematics, Springer Heidelberg 173
S. Hougardy (2006) Classes of perfect graphs Discrete Math. 306, 2529-2571
H. R. Maimani, M. R. Pournaki and S. Yassemi (2010) A class of weakly perfect graphs Czechoslovak Math. J. 60, 1037-1041
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