Graph labelings and cordiality

Abstract

In this paper we show that, if G and H are cordial and one has even size, then GU H is cordial; if G and H are cordial and both have even size, then G + H is cordial; if G and H are cordial and one has even size and either one has even order, then G + H is cordial; Cm U Cn is cordial if and only if m + n /≡ 2 (mod 4); mCn is cordial if and only if mn /≡ 2 (mod 4); Cm + Cn is cordial if and only if (m, n) /= (3, 3) and {m (mod 4), n (mod 4)} /= {0, 2}; and if Pk n is cordial, then n > k + 1 + √k − 2.We conjectures that this latter condition is also sufficient. He confirms the conjecture for k = 5, 6, 7, 8, and 9.