In this paper, by using the notion of fuzzy subsets, the concept of F-permutation is introduced. Then by applying this notion the concepts of presentation of an F-polygroup, graph of an F-permutation and F-permutation matrices are investigated.

let $g=(v,e)$ be a connected simple graph. a labeling $f:v to z_2$ induces two edge labelings $f^+, f^*: e to z_2$ defined by $f^+(xy) = f(x)+f(y)$ and $f^*(xy) = f(x)f(y)$ for each $xy in e$. for $i in z_2$, let $v_f(i) = |f^{-1}(i)|$, $e_{f^+}(i) = |(f^{+})^{-1}(i)|$ and $e_{f^*}(i) = |(f^*)^{-1}(i)|$. a labeling $f$ is called friendly if $|v_f(1)-v_f(0)| le 1$. for a friendly labeling $f$ of...

Acknowledgement Many efforts have been made for the completion of this project. However, it would not have been possible without the kind support and help of many individuals and organizations. I would like to extend my sincere thanks to all of them. I especially want to thank my Supervisor, Dr. Samir Al-khayatt, for his guidance during my research. His perpetual energy and enthusiasm in resear...

We study the behavior of two maps in an effort to better understand the stability of ωlimit sets ω(x, f ) as we perturb either x or f , or both. The first map is the set-valued function Λ taking f in C(I ,I) to its collection of ω-limit points Λ( f ) = ⋃x∈I ω(x, f ), and the second is the map Ω taking f in C(I ,I) to its collection of ω-limit sets Ω( f )= {ω(x, f ) : x ∈ I}.We characterize thos...