On a Connection of Number Theory with Graph Theory

An Application of Graph Theory to Additive Number Theory

A sequence of integers A = {a, < a2 < • • . < a„} is a Bzk) sequence if the number of representations of every integer as the sum of two distinct a,s is at most k . In this note we show that every B' sequence of n terms is a union of C2(k) • n 113 BzB (1) sequences, a nd tatthe re is aB (k) sequence of n terms which is not a union of cik • n'" 3 Bz" sequences. This solves a problem raised in 2 2

Segmentation of Magnetic Resonance Brain Imaging Based on Graph Theory

Introduction: Segmentation of brain images especially from magnetic resonance imaging (MRI) is an essential requirement in medical imaging since the tissues, edges, and boundaries between them are ambiguous and difficult to detect, due to the proximity of the brightness levels of the images. Material and Methods: In this paper, the graph-base...

On Proving that a Graph has no Large Clique: A Connection with Ramsey Theory

Uniform Number of a Graph

We introduce the notion of uniform number of a graph. The  uniform number of a connected graph $G$ is the least cardinality of a nonempty subset $M$ of the vertex set of $G$ for which the function $f_M: M^crightarrow mathcal{P}(X) - {emptyset}$ defined as $f_M(x) = {D(x, y): y in M}$ is a constant function, where $D(x, y)$ is the detour distance between $x$ and $y$ in $G$ and $mathcal{P}(X)$ ...

translation of collocations from english into persian, based on ghazalas theory

غزالا همایندها را به صورت ترکیبی از دو یا چند واژه که همواره در متون مختلف زبان ها همراه با هم می آیند تعریف می نماید. از دیدگاه او روند رو به رشد میل به ترجمه ی همایندها در مطالعات ترجمه، به دلیل اهمیت آنها در انسجام ساختار زبان است. این پایان نامه اساسا به ترجمه ی همایندها منحصر شده است. هدف آن بررسی کاربرد راهکارهای غزالا در مورد ترجمه ی همایندها از انگلیسی به فارسی است. هدف دیگر آن یافتن پر...