Mohammad Reza Fander - Azad University, Chaluse Branch

‎Let p be a prime number and n be a positive integer‎. ‎The graph‎ ‎G_p(n) is a graph with vertex set [n]=\{۱‎, ‎۲,\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.

perfect graph, Clique number, chromatic number