Constructive induction is the process of changing the representation of examples by creating new attributes from existing attributes. In classi cation, the goal of constructive induction is to nd a representation that facilitates learning a concept description by a particular learning system. Typically, the new attributes are Boolean or arithmetic combinations of existing attributes and the lea...

Let denote the Cartesian product of graphs and A total dominating set of with no isolated vertex is a set of vertices of such that every vertex is adjacent to a vertex in The total domination number of is the minimum cardinality of a total dominating set. In this paper, we give a new lower bound of total domination number of using parameters total domination, packing and -domination numbers of ...

A b-coloring of a graph G with k colors is a proper coloring of G using k colors in which each color class contains a color dominating vertex, that is, a vertex which has a neighbor in each of the other color classes. The largest positive integer k for which G has a b-coloring using k colors is the b-chromatic number b(G) of G. The b-spectrum Sb(G) of a graph G is the set of positive integers k...

A local coloring of a graph G is a function c : V (G) → N such that for each S ⊆ V (G), 2 ≤ |S| ≤ 3, there exist u, v ∈ S with |c(u) − c(v)| at least the size of the subgraph induced by S. The maximum color assigned by c is the value χl(c) of c, and the local chromatic number of G is χl(G) = min{χl(c) : c local coloring of G}. In this note the local chromatic number is determined for Cartesian ...

Strongly perfect graphs were introduced by C. Berge and P. Duchet in [1]. In [4], [3] the following was studied: the problem of strong perfectness for the Cartesian product, the tensor product, the symmetrical difference of n, n ≥ 2, graphs and for the generalized Cartesian product of graphs. Co-strong perfectness was first studied by G. Ravindra and D. Basavayya [5]. In this paper we discuss s...

In this paper we introduce the notion of bifuzzy ideals of K-algebras and investigate some interesting properties. Then we study the homomorphisms between the ideals of K-algebras and their relationship between the domains and the co-domains of the bifuzzy ideals under these homomorphisms. Finally the Cartesian product of bifuzzy ideals is discussed. Key–Words: Bifuzzy ideals; Characteristic; E...

The notions of intuitionistic fuzzy h-ideal and normal intuitionistic fuzzy h-ideal in Γ-hemiring are introduced and some of the basic properties of these ideals are investigated. Cartesian product of intuitionistic fuzzy h-ideals is also defined. Finally a characterization of intuitionistic fuzzy h-ideals in terms of fuzzy relations is obtained. Keywords—Γ-hemiring, fuzzy h-ideal, normal, cart...

The purpose of this paper is to study some properties of cartesian product of fuzzy completely prime ideals and fuzzy completely semiprime ideals of Γ-semigroups. Operator semigroups of a Γ-semigroup has been made to work by obtaining various relationships between cartesian product of fuzzy ideals (fuzzy completely prime ideals, fuzzy completely semiprime ideals) of a Γ-semigroup and that of it...

Let G be a graph and χaa(G) denotes the minimum number of colors required for an acyclic edge coloring of G in which no two adjacent vertices are incident to edges colored with the same set of colors. We prove a general bound for χaa(G□H) for any two graphs G and H. We also determine exact value of this parameter for the Cartesian product of two paths, Cartesian product of a path and a cycle, C...

In this paper simple formulae are derived for calculating the number of spanning trees of different product graphs. The products considered in here consists of Cartesian, strong Cartesian, direct, Lexicographic and double graph. For this purpose, the Laplacian matrices of these product graphs are used. Form some of these products simple formulae are derived and whenever direct formulation was n...