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Discrete Applied Mathematics, ISSN 0166-218X, 2018, Volume 251, pp. 204 - 220
Let G=(V,E) be a connected graph, let v∈V be a vertex and let e=uw∈E be an edge. The distance between the vertex v and the edge e is given by dG(e,v)=min{dG(u,v),dG(w,v)}. A vertex w... 
Edge metric dimension | Edge metric generator | Metric dimension | MATHEMATICS, APPLIED | RESOLVABILITY | Graphs | Mathematics | Graph theory | Comparative analysis | Apexes
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 03/2014, Volume 166, pp. 204 - 209
Journal Article
Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 05/2019, Volume 39, Issue 2, pp. 341 - 355
We demonstrate a construction of error-correcting codes from graphs by means of -resolving sets, and present a decoding algorithm which makes use of covering... 
94B25 | 05C12 | 94B35 | uncovering | 05B40 | resolving set | grid graph | metric dimension | covering design | error-correcting code | METRIC DIMENSION | MATHEMATICS | k-resolving set | k-metric dimension | UNCOVERINGS | GRAPHS
Journal Article
Applicable analysis and discrete mathematics, ISSN 1452-8630, 10/2016, Volume 10, Issue 2, pp. 501 - 517
A Roman dominating function on a graph 𝐺 is a function 𝑓: 𝑉 (𝐺) → {0, 1, 2} satisfying the condition that every vertex 𝑢 for which 𝑓(𝑢... 
Leaves | Literature | Mathematical theorems | Cardinality | Double stars | Discrete mathematics | Mathematical functions | Graph theory | Mathematical minima | Vertices | Roman domination | Total Roman domination | Total domination | Domina-tion | Domination | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 02/2018, Volume 38, Issue 1, pp. 287 - 299
Let = ( ) be a simple graph without isolated vertices and minimum degree , and let ∈ {1 − ⌈ /2⌉, . . . , ⌊ /2⌋} be an integer. Given a set ⊂ , a vertex of is... 
05C76 | alliances | domination | strong product graphs | 05C69 | open monopolies | Domination | Alliances | Strong product graphs | Open monopolies | MATHEMATICS
Journal Article
Information sciences, ISSN 0020-0255, 2019, Volume 473, pp. 87 - 100
Widespread usage of complex interconnected social networks such as Facebook, Twitter and LinkedInin modern internet era has also unfortunately opened the door... 
Privacy measure | Social networks | Active attack | Empirical evaluation | SET | SCALE-FREE | COMPUTER SCIENCE, INFORMATION SYSTEMS | GRAPHS | Privacy | Analysis | Computer Science - Social and Information Networks
Journal Article
The Electronic journal of combinatorics, ISSN 1077-8926, 07/2014, Volume 21, Issue 3
.... A set W of vertices of a connected graph Cc strongly resolves two different vertices x, y is not an element of W if either d(G)(x, W) = d(G)(x, y) + d(G)(y, W) or d(G)(y, W) = d(G)(y, x) + d(G)(x, W), where d(G)(x, W) = min {d(x, w... 
Strong partition dimension | Strong resolving graph | Strong metric dimension | Strong resolving partition | Strong resolving set | MATHEMATICS | DOUBLY RESOLVING SETS | MATHEMATICS, APPLIED | strong metric dimension | strong partition dimension | strong resolving graph | strong resolving set | strong resolving partition | RESOLVABILITY
Journal Article
Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 11/2016, Volume 36, Issue 4, pp. 1051 - 1064
Journal Article
Discrete mathematics, ISSN 0012-365X, 2016, Volume 339, Issue 7, pp. 1924 - 1934
Given a simple and connected graph G=(V,E), and a positive integer k, a set S⊆V is said to be a k-metric generator for G, if for any pair of different vertices u,v... 
Lexicographic product graphs | [formula omitted]-metric dimension | [formula omitted]-adjacency dimension | [formula omitted]-metric generator | k-adjacency dimension | k-metric dimension | k-metric generator | MATHEMATICS | CARTESIAN PRODUCTS
Journal Article
Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 02/2017, Volume 37, Issue 1, pp. 273 - 293
Let be a connected graph. Given an ordered set = { , . . . , } ⊆ ( ) and a vertex ∈ ( ), the representation of with respect to is the ordered -tuple ( ), ), .... 
05C76 | 05C12 | corona product graphs | rooted product graphs | metric dimension | primary subgraphs | metric basis | Metric basis | Corona product graphs | Rooted product graphs | Metric dimension | Primary subgraphs | MATHEMATICS | LEXICOGRAPHIC PRODUCT | HIERARCHICAL PRODUCT | RESOLVABILITY
Journal Article
Filomat, ISSN 0354-5180, 1/2016, Volume 30, Issue 11, pp. 3075 - 3082
The distance 𝑑(𝑢,𝑣) between two vertices 𝑢 and 𝑣 in a connected graph 𝐺 is the length of a shortest 𝑢 — 𝑣 path in 𝐺. A 𝑢 — 𝑣 path of length 𝑑(𝑢,𝑣) is called 𝑢 — 𝑣 geodesic. A set 𝑋 is convex in 𝐺... 
Leaves | Cardinality | Interval partitions | Geodesy | Discrete mathematics | Graph theory | Cartesianism | Combinatorics | Vertices | Geodetic sets | Convex domination | Graph partition | MATHEMATICS | graph partition | MATHEMATICS, APPLIED | NUMBER | geodetic sets | SETS | CARTESIAN PRODUCT
Journal Article
Filomat, ISSN 0354-5180, 1/2016, Volume 30, Issue 2, pp. 293 - 303
A dominating set of a graph 𝐺 which intersects every independent set of maximum cardinality in 𝐺... 
Integers | Cardinality | Mathematical sets | Polynomials | Graph theory | Vertices | Realizability | Domination | Transversal | Independent transversal domination | Independence | MATHEMATICS | MATHEMATICS, APPLIED | NUMBER | MAXIMUM STABLE SETS
Journal Article
Ars mathematica contemporanea, ISSN 1855-3966, 2015, Volume 9, Issue 1, pp. 19 - 25
Let G and H be two graphs with vertex sets V-1 = {u(1) , ..., u(n1)} and V-2 = {v(1) , ..., v(n2)}, respectively. If S subset of V-2, then the partial Cartesian product of G and H with respect to S is the graph G square H... 
Domination | Vizing's conjecture | Partial product of graphs | Cartesian product graph | Strong product graph | MATHEMATICS | strong product graph | MATHEMATICS, APPLIED | partial product of graphs
Journal Article
Rocznik Akademii Górniczo-Hutniczej im. Stanisława Staszica. Opuscula Mathematica, ISSN 1232-9274, 2016, Volume 36, Issue 5, pp. 575 - 588
Given a graph \(G=(V,E)\), the subdivision of an edge \(e=uv\in E(G)\) means the substitution of the edge \(e\) by a vertex \(x\) and the new edges \(ux\) and \(xv... 
Domination | Edge multisubdivision | Independent domination | Paired domination | Corona graph | Edge subdivision | independent domination | domination | edge multisubdivision | edge subdivision | corona graph | paired domination
Journal Article
Computer journal, ISSN 0010-4620, 08/2016, Volume 59, Issue 8, pp. 1264 - 1273
Journal Article
Bulletin of the Malaysian Mathematical Sciences Society, ISSN 0126-6705, 1/2016, Volume 39, Issue 1, pp. 199 - 217
A set S of vertices of a graph G is a dominating set in G if every vertex outside of S is adjacent to at least one vertex belonging... 
Domination | 05C76 | 05C12 | Domination-related parameters | Mathematics, general | Roman domination | Mathematics | Applications of Mathematics | Rooted product graphs | MATHEMATICS | VIZING-LIKE CONJECTURE | Graphs | Graph theory
Journal Article
Information sciences, ISSN 0020-0255, 01/2016, Volume 328, pp. 403 - 417
.... Let G=(V,E) be a simple connected graph and S={w1,…,wt}⊆V an ordered subset of vertices... 
Resolving set | Anonymity | Social network | Active attack | Graph | k-Metric antidimension | COMPUTER SCIENCE, INFORMATION SYSTEMS | ATTACK | NETWORKS | Privacy | Social networks | Algorithms | Analysis | Communities | Graphs | Graph theory | Representations | Impact analysis
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 05/2013, Volume 161, Issue 7-8, pp. 1022 - 1027
Let G be a connected graph. A vertex w strongly resolves a pair u, v of vertices of G if there exists some shortest u... 
Strong metric dimension | Clique number | Join graph | Corona product graph | Strong metric basis | Strong resolving set | MATHEMATICS, APPLIED | Coronas | Graphs | Mathematical models | Computation | Mathematical analysis | Invariants | Mathematics - Combinatorics
Journal Article
Carpathian Journal of Mathematics, ISSN 1584-2851, 1/2015, Volume 31, Issue 2, pp. 261 - 268
For an ordered subset S = {s₁, s₂, ...sk} of vertices in a connected graph G, the metric representation of a vertex u with respect to the set S is the k-vector r(u|S) = (dG(v, s₁), dG(v, s₂), ..., dG(v, sk)), where dG(x, y... 
Integers | Discrete mathematics | Cardinality | Combinatorics | Vertices | MATHEMATICS | strong product graph | MATHEMATICS, APPLIED | resolving set | metric dimension | Metric generator | metric basis
Journal Article
Resultate der Mathematik, ISSN 1420-9012, 2019, Volume 74, Issue 4, pp. 1 - 18
A quasi-total Roman dominating function on a graph $$G=(V, E)$$ G=(V,E) is a function $$f : V \rightarrow \{0,1,2\}$$ f:V→{0,1,2} satisfying... 
Mathematics, general | Mathematics | Quasi-total Roman domination number | Roman domination number | total Roman domination number | 05C69 | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
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