Edge Metric Dimension of Some Graph Operations
Sign Up to like & getrecommendations! Published in 2019 at "Bulletin of the Malaysian Mathematical Sciences Society"
DOI: 10.1007/s40840-019-00816-7
Abstract: Let $$G=(V, E)$$ G = ( V , E ) be a connected graph. Given a vertex $$v\in V$$ v ∈ V and an edge $$e=uw\in E$$ e = u w ∈ E , the… read more here.
Keywords: dimension graph; metric dimension; edge metric;
Metric Dimension of Maximal Outerplanar Graphs
Sign Up to like & getrecommendations! Published in 2019 at "Bulletin of the Malaysian Mathematical Sciences Society"
DOI: 10.1007/s40840-020-01068-6
Abstract: In this paper, we study the metric dimension problem in maximal outerplanar graphs. Concretely, if $$\beta (G)$$ β ( G ) denotes the metric dimension of a maximal outerplanar graph G of order n ,… read more here.
Keywords: outerplanar graphs; metric dimension; maximal outerplanar; dimension ... See more keywords
Metric basis and metric dimension of 1-pentagonal carbon nanocone networks
Sign Up to like & getrecommendations! Published in 2020 at "Scientific Reports"
DOI: 10.1038/s41598-020-76516-1
Abstract: Resolving set and metric basis has become an integral part in combinatorial chemistry and molecular topology. It has a lot of applications in computer, chemistry, pharmacy and mathematical disciplines. A subset S of the vertex… read more here.
Keywords: dimension pentagonal; basis; chemistry; metric basis ... See more keywords
Edge Metric Dimension and Edge Basis of One-Heptagonal Carbon Nanocone Networks
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DOI: 10.1109/access.2022.3158982
Abstract: A molecular (chemical) graph is a simple connected graph, where the vertices represent the compound’s atoms and the edges represent bonds between the atoms, and the degree (valence) of every vertex (atom) is not more… read more here.
Keywords: heptagonal carbon; carbon nanocone; edge metric; metric dimension ... See more keywords
The metric dimension of annihilator graphs of commutative rings
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Algebra and Its Applications"
DOI: 10.1142/s0219498820500899
Abstract: Let [Formula: see text] be a commutative ring with nonzero identity. The annihilator graph of [Formula: see text], denoted by [Formula: see text], is the (undirected) graph whose vertex set is the set of all… read more here.
Keywords: annihilator graphs; see text; metric dimension; formula see ... See more keywords
On the Fractional Metric Dimension of Convex Polytopes
Sign Up to like & getrecommendations! Published in 2021 at "Mathematical Problems in Engineering"
DOI: 10.1155/2021/3925925
Abstract: In order to identify the basic structural properties of a network such as connectedness, centrality, modularity, accessibility, clustering, vulnerability, and robustness, we need distance-based parameters. A number of tools like these help computer and chemical… read more here.
Keywords: dimension convex; metric dimension; fractional metric; convex polytopes ... See more keywords
Lexicographic metric spaces: Basic properties and the metric dimension
Sign Up to like & getrecommendations! Published in 2020 at "Applicable Analysis and Discrete Mathematics"
DOI: 10.2298/aadm180627004r
Abstract: In this article, we introduce the concept of lexicographic metric space and, after discussing some basic properties of these metric spaces, such as completeness, boundedness, compactness and separability, we obtain a formula for the metric… read more here.
Keywords: metric dimension; lexicographic metric; basic properties; properties metric ... See more keywords
Fault-tolerance in metric dimension of boron nanotubes lattices
Sign Up to like & getrecommendations! Published in 2023 at "Frontiers in Computational Neuroscience"
DOI: 10.3389/fncom.2022.1023585
Abstract: The concept of resolving set and metric basis has been very successful because of multi-purpose applications both in computer and mathematical sciences. A system in which failure of any single unit, another chain of units… read more here.
Keywords: boron nanotubes; tolerance metric; fault tolerance; metric dimension ... See more keywords
On Metric Dimensions of Symmetric Graphs Obtained by Rooted Product
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DOI: 10.3390/math6100191
Abstract: Let G = (V, E) be a connected graph and d(x, y) be the distance between the vertices x and y in G. A set of vertices W resolves a graph G if every vertex… read more here.
Keywords: graphs; dimensions symmetric; rooted product; metric dimension ... See more keywords
Edge Version of Metric Dimension and Doubly Resolving Sets of the Necklace Graph
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DOI: 10.3390/math6110243
Abstract: Consider an undirected and connected graph G = ( V G , E G ) , where V G and E G represent the set of vertices and the set of edges respectively. The concept… read more here.
Keywords: version metric; doubly resolving; dimension doubly; resolving sets ... See more keywords
On Rotationally Symmetrical Planar Networks and Their Local Fractional Metric Dimension
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DOI: 10.3390/sym15020530
Abstract: The metric dimension has various applications in several fields, such as computer science, image processing, pattern recognition, integer programming problems, drug discovery, and the production of various chemical compounds. The lowest number of vertices in… read more here.
Keywords: fractional metric; local fractional; metric dimension; dimension ... See more keywords