相关论文: On Sharp Bounds of Local Fractional Metric Dimensi…
Let $G$ be a graph, and let $u$, $v$, and $w$ be vertices of $G$. If the distance between $u$ and $w$ does not equal the distance between $v$ and $w$, then $w$ is said to resolve $u$ and $v$. The metric dimension of $G$, denoted $\beta(G)$,…
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…
The separation dimension of a graph $G$, written $\pi(G)$, is the minimum number of linear orderings of $V(G)$ such that every two nonincident edges are "separated" in some ordering, meaning that both endpoints of one edge appear before…
The metric dimension has been introduced independently by Harary, Melter and Slater in 1975 to identify vertices of a graph G using its distances to a subset of vertices of G. A resolving set X of a graph G is a subset of vertices such…
A vertex set $U \subseteq V$ of an undirected graph $G=(V,E)$ is a $\textit{resolving set}$ for $G$, if for every two distinct vertices $u,v \in V$ there is a vertex $w \in U$ such that the distances between $u$ and $w$ and the distance…
The metric dimension of a graph is the minimum size of a set of vertices such that each vertex is uniquely determined by the distances to the vertices of that set. Our aim is to upper-bound the order $n$ of a graph in terms of its diameter…
A set of vertices $S$ \emph{resolves} a connected graph $G$ if every vertex is uniquely determined by its vector of distances to the vertices in $S$. The \emph{metric dimension} of $G$ is the minimum cardinality of a resolving set of $G$.…
Metric dimension is a graph parameter that has been applied to robot navigation and finding low-dimensional vector embeddings. Throttling entails minimizing the sum of two available resources when solving certain graph problems. In this…
A set of vertices $S$ \emph{resolves} a graph $G$ if every vertex is uniquely determined by its vector of distances to the vertices in $S$. The \emph{metric dimension} of a graph $G$ is the minimum cardinality of a resolving set. In this…
The interaction between local traits and global frameworks of mathematical objects has long endured as a central theme in various mathematical domains. A graph \(G\) is referred to as locally linear provided that the subgraph induced by the…
This paper investigates fractional torsional rigidity on compact, connected metric graphs, a novel extension of the classical concept to nonlocal operators. The fractional torsional rigidity is defined as the $L^1$-norm of the fractional…
A set of vertices $W$ {\em resolves} a graph $G$ if every vertex of $G$ is uniquely determined by its vector of distances to the vertices in $W$. The {\em metric dimension} for $G$, denoted by $\dim(G)$, is the minimum cardinality of a…
The metric dimension is quite a well-studied graph parameter. Recently, the adjacency dimension and the local metric dimension have been introduced and studied. In this paper, we give a general formula for the local metric dimension of the…
The local minimum degree of a graph is the minimum degree that can be reached by means of local complementation. For any n, there exist graphs of order n which have a local minimum degree at least 0.189n, or at least 0.110n when restricted…
The metric (resp. edge metric) dimension of a simple connected graph $G$, denoted by dim$(G)$ (resp. edim$(G)$), is the cardinality of a smallest vertex subset $S\subseteq V(G)$ for which every two distinct vertices (resp. edges) in $G$…
Let $G$ be a graph with vertex set $V(G)$. For any two distinct vertices $x$ and $y$ of $G$, let $R\{x, y\}$ denote the set of vertices $z$ such that the distance from $x$ to $z$ is not equal to the distance from $y$ to $z$ in $G$. For a…
A set of vertices $W$ resolves a graph $G$ if every vertex is uniquely determined by its vector of distances to the vertices in $W$. A metric dimension of $G$ is the minimum cardinality of a resolving set of $G$. A bipartite graph G(n,n) is…
In the Metric Dimension problem, one asks for a minimum-size set $R$ of vertices such that for any pair of vertices of the graph, there is a vertex from $R$ whose two distances to the vertices of the pair are distinct. This problem has…
The metric dimension of a graph measures how uniquely vertices may be identified using a set of landmark vertices. This concept is frequently used in the study of network architecture, location-based problems and communication. Given a…
Graphlets are subgraphs rooted at a fixed vertex. The number of occurrences of graphlets aligned to a particular vertex, called graphlet degree sequence (gds), gives a topological description of the surrounding of the analyzed vertex.…