Classes of Planar Graphs with Constant Edge Metric Dimension
نویسندگان
چکیده
The number of edges in a shortest walk (without repetition vertices) from one vertex to another connected graph G is known as the distance between them. For id="M2"> x and an edge id="M3"> e = a b id="M4"> , minimum distances id="M5"> with id="M6"> id="M7"> said be id="M8"> id="M9"> . A id="M10"> distinguish (resolves) two distinct id="M11"> 1 id="M12"> 2 if id="M13"> id="M14"> different id="M15"> id="M16"> set id="M17"> X vertices id="M18"> metric generator for id="M19"> every id="M20"> are distinguished by some id="M21"> such smallest id="M22"> dimension id="M23"> In this article, we solve problem certain classes planar graphs.
منابع مشابه
On Cycle Related Graphs with Constant Metric Dimension
If is a connected graph, the distance between two vertices G , d u v , u v V G G is the length of a shortest path between them. Let be an ordered set of vertices of and let v be a vertex of . The representation 1 2 = , , , k W w w w G r v W of v with respect to is the -tuple W k 1 2 , , d v w , , , k d v w d v w , . If distinct vertices of have distinct repr...
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 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 کاملGraphs with Metric Dimension Two-A Characterization
In this paper, we define distance partition of vertex set of a graph G with reference to a vertex in it and with the help of the same, a graph with metric dimension two (i.e. 2 ) ( = G β ) is characterized. In the process, we develop a polynomial time algorithm that verifies if the metric dimension of a given graph G is two. The same algorithm explores all metric bases of graph G whenever 2 ) (...
متن کاملMetric Dimension for Random Graphs
The metric dimension of a graph G is the minimum number of vertices in a subset S of the vertex set of G such that all other vertices are uniquely determined by their distances to the vertices in S. In this paper we investigate the metric dimension of the random graph G(n, p) for a wide range of probabilities p = p(n).
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: Complexity
سال: 2021
ISSN: ['1099-0526', '1076-2787']
DOI: https://doi.org/10.1155/2021/5599274