On 2-Resolving Hop Dominating Sets in the Join, Corona and Lexicographic Product of Graphs
نویسندگان
چکیده

 Let G be a connected graph. A set S of vertices in is 2-resolving hop dominating if and for every vertex x ∈ V (G)\S there exists y such that dG(x, y) = 2. The minimum cardinality called the domination number denoted by γ2Rh(G). This study aims to combine concept with sets graphs. main results generated this include characterization join, corona lexicographic product two graphs, as well their corresponding bounds or exact values.
منابع مشابه
Some Dominating Sets of Lexicographic Product Graphs of Euler Totient Cayley Graphs with Arithmetic Graphs
The theory of domination in graphs is an emerging area of research in graph theory today. It has been studied extensively and finds applications to various branches of Science & Technology.Products are often viewed as a convenient language with which one can describe structures, but they are increasingly being applied in more substantial ways. In this paper, we consider lexicographic product gr...
متن کاملCharacterizations of minimal dominating sets and the well-dominated property in lexicographic product graphs
A graph is said to be well-dominated if all its minimal dominating sets are of the same size. In this work, we introduce the notion of an irreducible dominating set, a variant of dominating set generalizing both minimal dominating sets and minimal total dominating sets. Based on this notion, we characterize the family of minimal dominating sets in a lexicographic product of two graphs and deriv...
متن کاملOn graphs with disjoint dominating and 2-dominating sets
A DD2-pair of a graph G is a pair (D,D2) of disjoint sets of vertices of G such that D is a dominating set and D2 is a 2-dominating set of G. Although there are infinitely many graphs that do not contain a DD2-pair, we show that every graph with minimum degree at least two has a DD2-pair. We provide a constructive characterization of trees that have a DD2-pair and show that K3,3 is the only con...
متن کاملOn the strong metric dimension of corona product graphs and join graphs
Let G be a connected graph. A vertex w strongly resolves a pair u, v of vertices of G if there exists some shortest u− w path containing v or some shortest v − w path containing u. A set W of vertices is a strong resolving set for G if every pair of vertices of G is strongly resolved by some vertex of W . The smallest cardinality of a strong resolving set for G is called the strong metric dimen...
متن کاملOn unique minimum dominating sets in some Cartesian product graphs
Unique minimum vertex dominating sets in the Cartesian product of a graph with a complete graph are considered. We first give properties of such sets when they exist. We then show that when the first factor of the product is a tree, consideration of the tree alone is sufficient to determine if the product has a unique minimum dominating set.
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: European Journal of Pure and Applied Mathematics
سال: 2022
ISSN: ['1307-5543']
DOI: https://doi.org/10.29020/nybg.ejpam.v15i4.4585