Strength of strongest dominating sets in fuzzy graphs
A set S of vertices in a graph G=(V,E) is a dominating set ofG if every vertex of V-S is adjacent to some vertex of S.For an integer k≥1, a set S of vertices is a k-step dominating set if any vertex of $G$ is at distance k from somevertex of S. In this paper, using membership values of vertices and edges in fuzzy graphs, we introduce the concepts of strength of strongestdominating set as well as strength of strongest$k$-step dominating set in fuzzy graphs. We determine various bounds forthese parameters in fuzzy graphs. We also determine the strengthof strongest dominating set in some families of fuzzy graphsincluding complete fuzzy graphs and complete bipartite fuzzygraphs.
We consider the problem of incrementally computing a minimal dominating set of a directed graph after the insertion or deletion of a set of arcs. Earlier results have either focused on the study of the properties that minimum (not minimal) dominating sets preserved or lacked to investigate which update affects a minimal dominating set and in what ways. In this paper, we first show how to increm...متن کامل
Motivated by an application to unstructured multigrid calculations, we consider the problem of asymptotically minimizing the size of dominating sets in triangulated planar graphs. Speci cally, we wish to nd the smallest such that, for n su ciently large, every n-vertex planar graph contains a dominating set of size at most n. We prove that 1 4 13 , and we conjecture that = 14 . For triangulated...متن کامل
In this paper we study the size of generalised dominating sets in two graph processes which are widely used to model aspects of the world-wide web. On the one hand, we show that graphs generated this way have fairly large dominating sets (i.e. linear in the size of the graph). On the other hand, we present efficient strategies to construct small dominating sets. The algorithmic results represen...متن کامل
We give an efficient construction of a reasonably small dominating set in a circulant graph on n notes and k distinct chord lengths. This result is based on bounds on some double exponential sums.متن کامل
The concept of vague graph was introduced by Ramakrishna in . A vague graph is a generalized structure of a fuzzy graph that gives more precision, flexibility, and compatibility to a system when compared with systems that are designed using fuzzy graphs. The main purpose of this paper is to introduce the concept of dominating set, perfect dominating set, minimal perfect dominating set and i...متن کامل
A locating-dominating set a of graph G is a dominating set D of G with the additional property that every two distinct vertices outside D have distinct neighbors in D; that is, for distinct vertices u and v outside D, N(u) ∩D 6= N(v) ∩D where N(u) denotes the open neighborhood of u. A graph is twin-free if every two distinct vertices have distinct open and closed neighborhoods. The location-dom...متن کامل
دوره 6 شماره 2
صفحات 287- 297
تاریخ انتشار 2021-12-01
با دنبال کردن یک ژورنال هنگامی که شماره جدید این ژورنال منتشر می شود به شما از طریق ایمیل اطلاع داده می شود.