Some properties of prime graphs

Abstract

In this paper we show that, the union of stars Sm U Sn, are prime; the union of cycles and stars Cm U Sn are prime; Km U Pn is prime if and only if m is at most 3 or if m = 4 and n is odd; Kn corona K1 is prime if and only if n 6 7; Kn corona K2 is prime if and only if n <= 16; Km U Sn is prime if and only if the number of primes less than or equal to m + n + 1 is at least m; and that the complement of every prime graph with order at least 20 is not prime.