Results 11 to 20 of about 6,072 (265)
Partition Dimension of Generalized Petersen Graph
Complexity, 2021 Let G=VG,EG be the connected graph. For any vertex i∈VG and a subset B⊆VG, the distance between i and B is di;B=mindi,j|j∈B. The ordered k-partition of VG is Π=B1,B2,…,Bk. The representation of vertex i with respect to Π is the k-vector, that is, ri|Π=di,
Hassan Raza +3 more
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$k$-Efficient partitions of graphs [PDF]
Communications in Combinatorics and Optimization, 2019 A set $S = \{u_1,u_2, \ldots, u_t\}$ of vertices of $G$ is an efficient dominating set if every vertex of $G$ is dominated exactly once by the vertices of $S$.
M. Chellali +2 more
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Distance Domination in Vertex Partitioned Graphs
Mathematica Pannonica, 2022 We treat a variation of graph domination which involves a partition (V 1, V 2,..., Vk) of the vertex set of a graph G and domination of each partition class V i over distance d where all vertices and edges of G may be used in the domination process. Strict upper bounds and extremal graphs are presented; the results are collected in three handy tables ...
Frendrup, Allan +2 more
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Vertex partitions of chordal graphs [PDF]
Journal of Graph Theory, 2006 AbstractA k‐tree is a chordal graph with no (k + 2)‐clique. An ℓ‐tree‐partition of a graph G is a vertex partition of G into ‘bags,’ such that contracting each bag to a single vertex gives an ℓ‐tree (after deleting loops and replacing parallel edges by a single edge).
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Distributed Vertex-Cut Partitioning [PDF]
, 2014 Graph processing has become an integral part of big data analytics. With the ever increasing size of the graphs, one needs to partition them into smaller clusters, which can be managed and processed more easily on multiple machines in a distributed fashion. While there exist numerous solutions for edge-cut partitioning of graphs, very little effort has
Fatemeh Rahimian +3 more
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Which metrics for vertex-cut partitioning? [PDF]
2016 11th International Conference for Internet Technology and Secured Transactions (ICITST), 2016 In this paper we focus on vertex-cut graph partitioning and we investigate how it is possible to evaluate the quality of a partition before running the computation. To this purpose we scrutinize a set of metrics proposed in literature. We carry experiments with the widely-used framework for graph processing Apache GraphX and we perform an accurate ...
Mykhailenko, Hlib +2 more
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On the activities and partitions of the vertex subsets of graphs
Enumerative Combinatorics and Applications, 2021 Crapo introduced a construction of interval partitions of the Boolean lattice for sets equipped with matroid structure. This construction, in the context of graphic matroids, is related to the notion of edge activities introduced by Tutte. This implies that each spanning subgraph of a connected graph can be constructed from edges of exactly one ...
Kristina Dedndreaj, Peter Tittmann
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On Partition Dimension of Generalized Convex Polytopes
Journal of Mathematics, 2023 Let G be a graph having no loop or multiple edges, k−order vertex partition for G is represented by γ=γ1,γ2,…,γk. The vector rϕγ=dϕ,γ1,dϕ,γ2,dϕ,γ3⋯,dϕ,γk is the representation of vertex ϕ with respect to γ.
Syed Waqas Shah +5 more
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Vertex Separators for Partitioning a Graph [PDF]
Sensors, 2008 Finite Element Method (FEM) is a well known technique extensively studiedfor spatial and temporal modeling of environmental processes, weather predictioncomputations, and intelligent signal processing for wireless sensors. The need for hugecomputational power arising in such applications to simulate physical phenomenoncorrectly mandates the use of ...
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On the b-Domatic Number of Graphs
Discussiones Mathematicae Graph Theory, 2019 A set of vertices S in a graph G = (V, E) is a dominating set if every vertex not in S is adjacent to at least one vertex in S. A domatic partition of graph G is a partition of its vertex-set V into dominating sets. A domatic partition 𝒫 of G is called b-
Benatallah Mohammed +2 more
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