In combinatorics, a latin square is $$n\times n$$ matrix filled with n different symbols, each occurring exactly once in row and column. Associated to square, we can define simple graph called graph. this article, compute lower upper bounds for the domination number k-tuple total numbers of such graphs. Moreover, describe formula 2-tuple number.

The structure generating function of a language enumerates the number of distinct words contained in the language with respect to their length. Given any unambiguous tuple grammar, a method is described which yields a system of equations, whose unique solution is the structure generating function. The entropy (channel capacity) is an important information theoretic quantity associated with a la...

NP-complete problems cannot have efficient algorithms unless P = NP. Due to their importance in practice, however, it is useful to improve the known exponential-time algorithms for NP-complete problems. We survey some of the recent results on such improved exponential-time algorithms for the NP-complete problems satisfiability, graph colorability, and the domatic number problem. The determinist...

A k-tuple coloring of a graph G assigns a set of k colors to each vertex of G so that if two vertices are adjacent, the corresponding sets of colors are disjoint. The k-tuple chromatic number of G is the smallest t so that there is such a k-tuple coloring of G using t colors in all. The Kneser graph K(m,n) has as vertices all n-element subsets of the set {1,2, . . . ,m} and an edge between two ...

The tuple space coordination model, originally introduced in the Linda programming language [2], uses a shared memory object called a tuple space to support coordination that is decoupled both in time – processes do not have to be active at the same time – and space – processes do not need to know each others’ addresses. The tuple space can be considered to be a kind of storage that stores tupl...

A k-tuple coloring of a graph G assigns a set of k colors to each vertex of G such that if two vertices are adjacent, the corresponding sets of colors are disjoint. The k-tuple chromatic number of G, χk(G), is the smallest t so that there is a k-tuple coloring of G using t colors. It is well known that χ(G2H) = max{χ(G), χ(H)}. In this paper, we show that there exist graphs G and H such that χk...

In this paper, a necessary and sufficient condition for the existence of an efficient 2-dominating set in a class of circulant graphs has been obtained and for those circulant graphs, an upper bound for the 2domination number is also obtained. For the circulant graphs Cir(n,A), where A = {1, 2, . . . , x, n − 1, n − 2, . . . , n − x} and x ≤ bn−1 2 c, the perfect 2-tuple total domination number...