The main contribution of this work is a new type of graph product, which we call the zig-zag product. Taking a product of a large graph with a small graph, the resulting graph inherits (roughly) its size from the large one, its degree from the small one, and its expansion properties from both! Iteration yields simple explicit constructions of constant-degree expanders of arbitrary size, startin...

In this paper, a general expression of the Shapley value for fuzzy games on vague sets is proposed, where the player participation levels are vague sets. The existence and uniqueness of the given Shapley value are showed by establishing axiomatic system. When the fuzzy games on vague sets are convex, the given Shapley value is a vague population monotonic allocation function (VPMAF) and an elem...

In this paper, we have studied the connectedness of the graphs on the direct product of the Weyl groups. We have shown that the number of the connected components of the graph on the direct product of the Weyl groups is equal to the product of the numbers of the connected components of the graphs on the factors of the direct product. In particular, we show that the graph on the direct product o...

This paper reports a new idea-screening method for new product development (NPD) with a group of decision makers having imprecise, inconsistent and uncertain preferences. The traditional NPD analysis method determines the solution using the membership function of fuzzy sets which cannot treat negative evidence. The advantage of vague sets, with the capability of representing negative evidence, ...

A graph is said to be cordial if it has 0 - 1 labeling which satisfies particular conditions. In this paper, we construct the corona between paths and second power of fan graphs explain necessary sufficient conditions for construction cordial.

Recent work of Gromov, Epstein, Cannon, Thurston and many others has generated strong interest in the geometric and algorithmic structure of finitely generated infinite groups. (See [16],[17] and [14].) Many of these structures are preserved by taking graph products. The graph product of groups (not to be confused with the fundamental group of a graph of groups) is a product mixing direct and f...

A graph structure is a useful tool in solving the combinatorial problems in different areas of computer science and computational intelligence systems. A bipolar fuzzy graph structure is a generalization of a bipolar fuzzy graph. In this paper, we present several different types of operations, including composition, Cartesian product, strong product, cross product, and lexicographic product on ...

Let Λ(n) be the smallest number so that there are two n chromatic graphs whose product has chromatic number Λ(n). Under the assumption that a certain sharper result than one obtained by Duffus, Sands and Woodrow [1] holds we will prove that Λ(n) ≥ n/2. MR Subject Classifications [2000]: 05C15 Keyworks: chromatic number, graph product, Hedeniemi conjecture

The edge-bandwidth of a graph G is the bandwidth of the line graph of G. We show asymptotically tight bounds on the edge-bandwidth of two dimensional grids and tori, the product of two cliques and the n-dimensional hypercube.

We obtain some improved upper and lower bounds on the oriented chromatic number for different classes of products of graphs.