A signed graph is a simple with two types of edges. Switching vertex v corresponds to changing the type each edge incident v. homomorphism from G another H mapping φ:V(G)→V(H) such that, after switching any number vertices G, φ maps every an same in H. The chromatic χs(G) order smallest that there We show triangular grids at most 10 and hexagonal 4.

in this paper, a numerical method for nding minimal solution of a mn fullyfuzzy linear system of the form ax = b based on pseudo inverse calculation,is given when the central matrix of coecients is row full rank or column fullrank, and where a~ is a non-negative fuzzy mn matrix, the unknown vectorx is a vector consisting of n non-negative fuzzy numbers and the constant b isa vector consisti...

In this paper, we study the existence, asymptotic behavior of the positive solutions of a fuzzy nonlinear difference equation$$ x_{n+1}=frac{Ax_n+x_{n-1}}{B+x_{n-1}}, n=0,1,cdots,$$ where $(x_n)$ is a sequence of positive fuzzy number, $A, B$ are positive fuzzy numbers and the initial conditions $x_{-1}, x_0$ are positive fuzzy numbers.

The purpose of this study is to find the percentiles of fuzzy numbersand to demonstrate their applications, which include finding weightedmeans, dispersion indices, and the percentile intervals of fuzzy numbers. Thecrisp approximations of fuzzy numbers introduced in this paper are new andinteresting for the comparison of fuzzy environments, such as a variety of economic,financial, and engineeri...

recently, abbasbandy and asady have been proposed a modificationof the distance based approach, namely ``sign distance method''.however, in this paper, it is shown that this method has some drawbacks, i.e.,the result is not consistent with human intuition for specialcases and this method cannot always logically infer rankingorder of the images of the fuzzy numbers. in this paper, wepresent a re...

this study is an investigation of fuzzy linear regression model for crisp/fuzzy input and fuzzy output data. a least absolutes deviations approach to construct such a model is developed by introducing and applying a new metric on the space of fuzzy numbers. the proposed approach, which can deal with both symmetric and non-symmetric fuzzy observations, is compared with several existing models by...