Eternal Independent Sets in Graphs
نویسندگان
چکیده
منابع مشابه
INDEPENDENT SETS OF SOME GRAPHS ASSOCIATED TO COMMUTATIVE RINGS
Let $G=(V,E)$ be a simple graph. A set $Ssubseteq V$ isindependent set of $G$, if no two vertices of $S$ are adjacent.The independence number $alpha(G)$ is the size of a maximumindependent set in the graph. In this paper we study and characterize the independent sets ofthe zero-divisor graph $Gamma(R)$ and ideal-based zero-divisor graph $Gamma_I(R)$of a commutative ring $R$.
متن کاملEternal 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 کاملEternal 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 کاملCounting independent sets in graphs
In this short survey article, we present an elementary, yet quite powerful, method of enumerating independent sets in graphs. This method was first employed more than three decades ago by Kleitman and Winston and has subsequently been used numerous times by many researchers in various contexts. Our presentation of the method is illustrated with several applications of it to ‘real-life’ combinat...
متن کاملIndependent Sets in Polarity Graphs
Given a projective plane Σ and a polarity θ of Σ, the corresponding polarity graph is the graph whose vertices are the points of Σ, and two distinct points p1 and p2 are adjacent if p1 is incident to p θ 2 in Σ. A well-known example of a polarity graph is the Erdős-Rényi orthogonal polarity graph ERq, which appears frequently in a variety of extremal problems. Eigenvalue methods provide an uppe...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Theory and Applications of Graphs
سال: 2016
ISSN: 2470-9859
DOI: 10.20429/tag.2016.030103