The local metric dimension of split and unicyclic graphs
نویسندگان
چکیده
A set <em>W</em> is called a local resolving of <em>G</em> if the distance <em>u</em> and <em>v</em> to some elements are distinct for every two adjacent vertices in <em>G</em>. The metric dimension minimum cardinality connected graph split <em>V</em>(<em>G</em>) can be partitioned into subsets <em>V</em><sub>1</sub> <em>V</em><sub>2</sub> where an induced subgraph G by complete independent set, respectively. We also consider graph, namely unicyclic which containing exactly one cycle. In this paper, we provide general sharp bounds graph. determine exact value any graphs.
منابع مشابه
The metric dimension and girth of graphs
A set $Wsubseteq V(G)$ is called a resolving set for $G$, if for each two distinct vertices $u,vin V(G)$ there exists $win W$ such that $d(u,w)neq d(v,w)$, where $d(x,y)$ is the distance between the vertices $x$ and $y$. The minimum cardinality of a resolving set for $G$ is called the metric dimension of $G$, and denoted by $dim(G)$. In this paper, it is proved that in a connected graph $...
متن کاملthe metric dimension and girth of graphs
a set $wsubseteq v(g)$ is called a resolving set for $g$, if for each two distinct vertices $u,vin v(g)$ there exists $win w$ such that $d(u,w)neq d(v,w)$, where $d(x,y)$ is the distance between the vertices $x$ and $y$. the minimum cardinality of a resolving set for $g$ is called the metric dimension of $g$, and denoted by $dim(g)$. in this paper, it is proved that in a connected graph $...
متن کاملThe Local Metric Dimension of Cyclic Split Graph
Let , be a graph with vertex set and edge set . Let then is said to be a local metric basis of , if for any two adjacent vertices , ⁄ , there exists a such that , , . The minimum cardinality of local metric basis is called the local metric dimension (lmd) of graph G. In this paper we investigate the local metric basis and local metric dimension of Cyclic Split Graph .
متن کاملThe Hyper-Zagreb Index of Trees and Unicyclic Graphs
Topological indices are widely used as mathematical tools to analyze different types of graphs emerged in a broad range of applications. The Hyper-Zagreb index (HM) is an important tool because it integrates the first two Zagreb indices. In this paper, we characterize the trees and unicyclic graphs with the first four and first eight greatest HM-value, respectively.
متن کاملOn the metric dimension of Grassmann graphs
The metric dimension of a graph Γ is the least number of vertices in a set with the property that the list of distances from any vertex to those in the set uniquely identifies that vertex. We consider the Grassmann graph Gq(n,k) (whose vertices are the k-subspaces of Fq, and are adjacent if they intersect in a (k− 1)-subspace) for k ≥ 2. We find an upper bound on its metric dimension, which is ...
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: Indonesian journal of combinatorics
سال: 2022
ISSN: ['2541-2205']
DOI: https://doi.org/10.19184/ijc.2022.6.1.3