Bounding the Security Number of a Graph

نویسندگان

  • G Gordon Worley
  • Ronald D. Dutton
  • Matt Gordon
چکیده

Given a graph G, the security number of G is the cardinality of a minimum secure set of G, the smallest set of vertices S ⊆ V (G) such that for all X ⊆ S, |N [X] ∩ S| ≥ |N [X] − S|. It is believed to be computationally difficult to find the security number of large graphs, so we present techniques for reducing the difficulty of both finding a secure set and determining bounds on the security number.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Bounding cochordal cover number of graphs via vertex stretching

It is shown that when a special vertex stretching is applied to a graph, the cochordal cover number of the graph increases exactly by one, as it happens to its induced matching number and (Castelnuovo-Mumford) regularity. As a consequence, it is shown that the induced matching number and cochordal cover number of a special vertex stretching of a graph G are equal provided G is well-covered bipa...

متن کامل

Security Analysis of the Distance Bounding Protocol Proposed by Jannati and Falahati

In this paper, the security of a distance bounding protocol is analyzed which has been recently proposed by Jannati and Falahati (so-called JF). We prove that an adversary can recover key bits of JF protocol with probability of “1” while the complexity of attack is “2n” runs of protocol. In addition, we propose an improved protocol and prove that the improved protocol is resistant to mafia frau...

متن کامل

Eternal m- Security Subdivision Numbers in Graphs

Let  be a simple graph with vertex set  and edges set . A set  is a dominating set if every vertex in  is adjacent to at least one vertex  in . An eternal 1-secure set of a graph G is defined as a dominating set  such that for any positive integer k and any sequence  of vertices, there exists a sequence of guards   with  and either  or  and  is a dominating set. If we take a guard on every ver...

متن کامل

Eternal m-security subdivision numbers in graphs

An eternal $m$-secure set of a graph $G = (V,E)$ is aset $S_0subseteq V$ that can defend against any sequence ofsingle-vertex attacks by means of multiple-guard shifts along theedges of $G$. A suitable placement of the guards is called aneternal $m$-secure set. The eternal $m$-security number$sigma_m(G)$ is the minimum cardinality among all eternal$m$-secure sets in $G$. An edge $uvin E(G)$ is ...

متن کامل

On the computational complexity of finding a minimal basis for the guess and determine attack

Guess-and-determine attack is one of the general attacks on stream ciphers. It is a common cryptanalysis tool for evaluating security of stream ciphers. The effectiveness of this attack is based on the number of unknown bits which will be guessed by the attacker to break the cryptosystem. In this work, we present a relation between the minimum numbers of the guessed bits and uniquely restricted...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2006