Let G = (V,E) be a locally finite graph, i.e. a graph in which every vertex has finitely many adjacent vertices. In this paper, we associate a topology to G, called graphic topology of G and we show that it is an Alexandroff topology, i.e. a topology in which intersec- tion of every family of open sets is open. Then we investigate some properties of this topology. Our motivation is to give an e...

in this paper, we introduce the concepts of right, left and product stabilizers on hoops and study some properties and the relation between them.  and we try to find that how they can be equal and investigate that under what condition they can be filter, implicative filter, fantastic and positive implicative filter. also, we prove that  right and product stabilizers are filters and if they are ...

Recent work has shown that the physical connectivity of the Internet exhibits small-world behavior. Characterizing such behavior is important not only for generating realistic Internet topology, but also for the proper evaluation of large-scale content delivery techniques. Along this line, this paper tries to explain how the small-world behavior arises in the Internet topologies and how it impa...

The concept of small worlds is introduced into the physical topology of wireless networks in this work. A. Helmy provided two construction schemes of small worlds for the wireless networks, link rewiring and link addition, but he mainly focused on the virtual topology. Based on the broadcasting nature of the radio transmission, we propose a construction scheme of small worlds for the physical t...

In a graph with a small world topology nodes are highly clustered yet the path length be tween them is small Such a topology can make search problems very di cult since local deci sions quickly propagate globally We show that graphs associated with many di erent search problems have a small world topology and that the cost of solving such search problems can have a heavy tailed distribution The...

in this paper we investigate generalized topologies generated by a subbase ofpreorder relators and consider its application in the concept of the complement. we introducethe notion of principal generalized topologies obtained from the new type of open sets andstudy some of their important properties.

Small world topology has been receiving much attention recent years. Many real-world graphs actually have a small world topology. In a small world graph, a shortcut plays an important role to make the world small; if shortcuts are eliminated, the graph is separated into clusters. In this paper, I propose a new clustering algorithm by eliminating “shortcuts,” which helps a user understand the gr...

I INTRODUCTION The recent emergence of novel network applications such as Gnutella, Freenet, and Napster has reincarnated the familiar peer-to-peer (P2P) architecture model of the original Internet in new and innovative ways in an effort to facilitate worldwide sharing of information [1]. As a result, there is an ever-increasing need for distributed protocols that would allow peer-to-peer appli...