WebThe metric dimension of G is the minimum cardinality of a resolving set of G. Let G β, D be the set of graphs with metric dimension β and diameter D. It is well-known that the minimum order of a graph in G β, D is exactly β + D. The first contribution of this paper is to characterise the graphs in G β, D with order β + D for all values of β and D. 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. These invariants are examined, especially how they relate to one another and to other graph invariants and their behaviour in certain graph classes.
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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 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 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 … 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 … Meer weergeven WebI received my PhD in Computer Science, entitled "Inexact graph matching: Application to 2D and 3D Pattern Recognition", in December 2016, at LIRIS laboratory and Claude Bernard Lyon 1 University (France). I received a Master’s degree in Computer Science, specialty: Engineering of Artificial Intelligence at Montpellier 2 University (France). During my PhD, … switching voicemail off on iphone
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WebMetric graphs are often introduced based on combinatorics, upon “associat- ing” each edge of a graph with an interval; or else, casually “gluing” a collection of intervals at their … WebTheorem 3.1. For all integers D > 2 and β > 1, the maximum order of a connected graph with diameter D and metric dimension β is u0012u0016 u0017 u0013β dD/3e 2D X +1 +β (2i − 1)β−1 . (2) 3 i=1 First we prove the upper bound in Theorem 3.1. Lemma 3.2. WebGraph Measures & Metrics The Wolfram Language supports a broad range of measures that characterize graphs, from simple measures, such as the number of vertices and … switching visa in the uk