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.
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
Fander, M. R. (2015). Chromatic and clique numbers of a class of perfect graphs. Transactions on Combinatorics, 4(4), 1-4. doi: 10.22108/toc.2015.7340
MLA
Mohammad Reza Fander. "Chromatic and clique numbers of a class of perfect graphs". Transactions on Combinatorics, 4, 4, 2015, 1-4. doi: 10.22108/toc.2015.7340
HARVARD
Fander, M. R. (2015). 'Chromatic and clique numbers of a class of perfect graphs', Transactions on Combinatorics, 4(4), pp. 1-4. doi: 10.22108/toc.2015.7340
VANCOUVER
Fander, M. R. Chromatic and clique numbers of a class of perfect graphs. Transactions on Combinatorics, 2015; 4(4): 1-4. doi: 10.22108/toc.2015.7340
)
