Abstract. Let n 1 = ef + 1 and n 2 = ef ′ + 1 be two distinct odd primes with positive integers e, f, f ′ . In this paper, the two-prime Whiteman's generalized cyclotomic sequence of order e = 6 is employed to construct several classes of cyclic codes over GF(q) with length n 1 n 2 . The lower bounds on the minimum distance of these cyclic codes are obtained.

Although for more than 20 years, Whiteman’s generalized cyclotomic sequences have been thought of as the most important pseudo-random sequences, but, there are only a few papers in which their 2-adic complexities have been discussed. In this paper, we construct a class of binary sequences of order four with odd length (product of two distinct odd primes) from Whiteman’s generalized cyclotomic classes. After that, we determine both 2-adic complexity and linear complexity of these sequences. Our results show that these complexities are greater than half of the period of the sequences, therefore, it may be good pseudo-random sequences.

Let G=(V,E) be a simple, finite, connected and undirected graph. A non-empty subset D of V(G) in a graph G=(V,E) is a dominating set if every vertex in V-D is adjacent to atleast one vertex in D. The domination number γ(G) of G is the minimum cardinality of a minimal dominating set of G. A non-empty subset D of V(G) is called an equitable dominating set of a graph G if for every, there exists a vertex such that and . The minimum cardinality of such a minimal dominating set is denoted by γ e (G) and is called an equitable domination number of G. A dominating set D of graph G is called a split dominating set, if the induced subgraph is disconnected. Let denote the greatest integer not greater than and denote the least integer not less than x . In this paper, we investigated the split, inverse and equitable domination number of the middle and the central graphs of the path P n and the cycle C n