Metric dimensions of a graph
Web1 jan. 2010 · The distance between two vertices is the basis of the definition of several graph parameters including diameter, radius, average distance and metric dimension. … Web1 aug. 2024 · A metric generator of minimum cardinality is called a metric basis for G and its cardinality is the metric dimension of G, which is denoted by dim ( G ). These concepts were introduced by Slater in [ 14] in connection with some location problems in graphs.
Metric dimensions of a graph
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WebThe metric dimension (Tillquist et al. 2024) or (Tomescu and Javid 2007, Ali et al. 2016) of a graph is the smallest number of nodes required to identify all other nodes based on shortest path distances uniquely. More explicitly, following Foster-Greenwood and Uhl (2024), let be a finite connected graph with vertex set . Web15 okt. 2000 · The metric dimension dim(G) of G is the minimum cardinality of a resolving set for G. Bounds on dim(G) are presented in terms of the order and the diameter of G. …
WebWe established that a generalized Petersen graph P(n, 2) has a mixed metric dimension equivalent to 4 for n ≡ 0, 2(mod4), and, for n ≡ 1, 3(mod4), the mixed metric dimension is 5. We thus determine that each graph of the family of a generalized Petersen graph P(n, 2) has a constant mixed metric dimension.2010 Mathematics Subject Classification: … Web1 apr. 2013 · In graph theory, metric dimension is a parameter that has appeared in various applications, as diverse as network discovery and verification [2], …
WebIn the present study, cylindrical ABS P400 polymer parts (diameter 6.5 mm) to be used as die-sinking EDM (electric discharge machining) novel electrodes were fabricated using a fused deposition modeling (FDM) process. To meet the conductivity requirement in EDM, ABS parts were metallized using an innovative method that comprised putting … Web21 okt. 2024 · The metric dimension of a graph is the smallest number of vertices from which the vector of distances to every vertex in the graph is unique. It may be …
In graph theory, the metric dimension of a graph G is the minimum cardinality of a subset S of vertices such that all other vertices are uniquely determined by their distances to the vertices in S. Finding the metric dimension of a graph is an NP-hard problem; the decision version, determining whether the … Meer weergeven For an ordered subset $${\displaystyle W=\{w_{1},w_{2},\dots ,w_{k}\}}$$ of vertices and a vertex v in a connected graph G, the representation of v with respect to W is the ordered k-tuple Meer weergeven In Chartrand et al. (2000), it is proved that: • The metric dimension of a graph G is 1 if and only if G is a path. • The metric dimension of an n-vertex graph is n − 1 if and only if it is a complete graph. • The metric dimension of an n-vertex graph is n − 2 if and … Meer weergeven If a tree is a path, its metric dimension is one. Otherwise, let L denote the set of leaves, degree-one vertices in the tree. Let K be the set of vertices that have degree greater than … Meer weergeven Decision complexity Deciding whether the metric dimension of a graph is at most a given integer is NP-complete. It remains NP-complete for bounded … Meer weergeven
Web1 dec. 2014 · A metric generator is a set W of vertices of a graph such that for every pair of vertices of G, there exists a vertex with the condition that the length of a shortest path from u to w is different from the length of a shortest path from v to w. In this case the vertex w is said to resolve or distinguish the vertices u and v. over bed canopy queenWebIt was observed in [] that the metric dimension problem is NP-complete for planar graphs.Diaz et al. also proposed an algorithm to calculate the metric dimension of … overbed bookcaseWebApril 14, 2024 - 154 likes, 3 comments - ARCHITECTURE INTERIOR DESIGN (@archi_place) on Instagram: "Some bathroom design illustrations from “GRAPHIC GUIDE TO ... over bed art ideasWeb20 nov. 2024 · The Metric Dimension of Circulant Graphs - Volume 60 Issue 1. To save this article to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. rally project management tool tutorialWeb11 apr. 2024 · This paper is devoted to the study of the arithmetic graph of a composite number m, denoted by A m . It has been observed that there exist different composite … overbed cartWeb10 jan. 2016 · Let G = (V, E) be a connected graph. A vertex v ∈ V is said to resolve two vertices x and y if d G (v, x) ≠ d G (v, y).A set S ⊆ V is said to be a metric generator for … rallyproshopWeb15 nov. 2024 · They each should be used in pair with domain knowledge of the data you’re modeling as a graph. Graph Summary: Number of nodes : 115 Number of edges : 613 … rally proserpina 2022