Metric dimension of graphs
WebThe metric dimension problem (MDP) of computing the metric dimension of graphs is a kind of complex combinatorial optimization problem. In this paper, a hybrid algorithm for solving the MDP is developed, through which the metric base of graphs can be learned, and consequently the metric dimension of graphs is estimated. 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 … 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 … Meer weergeven
Metric dimension of graphs
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WebThe smallest cardinality of a mixed metric generator for G is called the mixed metric dimension and is denoted by dimm (G). In this paper we consider the structure of mixed metric generators and characterize graphs for which the mixed metric dimension equals the trivial lower and upper bounds. Web1 mei 2004 · We study generators of metric spaces—sets of points with the property that every point of the space is uniquely determined by the distances from their elements. Such generators put a light on seemingly different kinds of problems in combinatorics that are not directly related to metric spaces.
Web20 dec. 2024 · The concept of the metric dimension of a graph was birthed independently by Harary and Melter in 1976 and by Slater in 1975, and is now well studied in graph … WebI am proficient in multiple programming languages and frameworks and capable of utilizing cloud providers. I am able to enhance a given system's value in multiple dimensions like analytics, metrics, machine learning, recommending, personalization, and more. Languages: Javascript (, HTML, CSS), Typescript, SQL, Python, Java, Solidity, C, C++, …
WebOn Wed, April 22th, 2024, 2pm CET, Pierre PARREND (Laboratoire de Recherche de l’EPITA / Laboratoire ICube – Unistra), will talk about “Trusted Graph for explainable detection of ... WebThe size of a dominant edge metric basis of G is denoted by Ddime ( G ) and is called the dominant edge metric dimension. In this paper, the concept of dominant edge metric dimension (DEMD for short) is introduced and its basic properties are studied. Moreover, NP-hardness of computing DEMD of connected graphs is proved.
Webwww.ejgta.org Electronic Journal of Graph Theory and Applications 11 (1) (2024), 197–208 The dominant edge metric dimension of graphs Mostafa Tavakolia, Meysam Korivand …
WebThe metric dimension problem (MDP) of computing the metric dimension of graphs is a kind of complex combinatorial optimization problem. In this paper, a hybrid algorithm for … trimana 90045WebIn this paper, the mixed metric dimension of a generalized Petersen graph P ( n, 2) is calculated. We established that a generalized Petersen graph P ( n, 2) has a mixed metric dimension equivalent to 4 for n ≡ 0, 2 ( mod 4), and, for n ≡ 1, 3 ( mod 4), the mixed metric dimension is 5. trimanje psaWeb31 dec. 2024 · The edge metric dimension of graph is the minimum cardinality of edge resolving set, say , and is denoted as . An edge metric generator for of cardinality is an … trimazepinehttp://www.scholarpedia.org/article/Metric_Dimension trimco tavira ii flat glass slim serve overWebIt 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 outerplanar graphs in polynomial time. Since bicyclic graphs of type I and type II are also outerplanar graphs, their metric dimension can also be calculated in polynomial time. trimazole drugWeb2 feb. 2024 · Metric Dimension Resolving Set Circulant Graphs Minimum Cardinality Vertex Set Let G be a connected graph with vertex set V (G) and d (u,v) be the distance between the vertices u and v. trimeprazine brand nameWeb15 sep. 2013 · A metric ISO screw thread is designated by the letter M followed by the value of the nominal diameter D (the maximum thread diameter) and the pitch P, both expressed in millimetres and separated by the multiplication sign, × (e.g. M8×1.25). If the pitch is the normally used "coarse" pitch listed in ISO 261 or ISO 262, it can be omitted … trimane kimbrough