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On the partition dimension of a class of circulant graphs

Information Processing Letters, 2014
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Cyriac Grigorious, Sudeep Stephen, Mirka Miller   +2 more
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On the Partition Dimension of Circulant Graphs

The Computer Journal, 2016
For a vertex v of a connected graph G ( V , E ) and a subset S of V , the distance between v and S is defined by d ( v , S )=min{ d ( v , x ):x∈ S }. For an ordered k .-partition Π={ S 1 , S 2 ,…, S k } of V , the representation of v with respect to Π is the k -vector r ( v ∣Π)=( d ( v , S 1 ), d ( v , S 2 ),…, d ( v , S k )).
Cyriac Grigorious, Sudeep Stephen, Bharati Rajan, Mirka Miller   +3 more
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The Wästlund Partition in Higher Dimensions

The American Mathematical Monthly, 2020
We prove that the set {(x1,x2,…,xd)∈R≥0d;:;x1p+x2p+⋯+xdp≤1} has volume Γ(1+1/p)d/Γ(1+d/p) using a partition of the positive orthant, which we name in honor of Wastlund.
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The number of guillotine partitions in d dimensions

Information Processing Letters, 2006
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Eyal Ackerman, Gill Barequet, Ron Y. Pinter, Dan Romik   +3 more
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On 2-partition dimension of the circulant graphs

Journal of Intelligent & Fuzzy Systems, 2021
The partition dimension is a variant of metric dimension in graphs. It has arising applications in the fields of network designing, robot navigation, pattern recognition and image processing. Let G (V (G) , E (G)) be a connected graph and Γ = {P1, P2, …, Pm} be an ordered m-partition of V (G).
Asim Nadeem, Agha Kashif, Sohail Zafar, Zohaib Zahid   +3 more
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Computation of Metric Dimension and Partition Dimension of Nanotubes

Journal of Computational and Theoretical Nanoscience, 2015
Muhammad Kamran Siddiqui, Muhammad Imran   +1 more
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Partitioned Dimension: Modeling the Numerical Dimension in Data Warehouse

2010 12th International Asia-Pacific Web Conference, 2010
In the traditional data warehouse modeling, a numerical attribute with continuous data are not suitable for modeling as a dimension, unless it is partitioned into a concept hierarchy according to some predefined mapping-rules. In some cases, such rules are flexible or unavailable, so the partitioned dimension is proposed in this paper as the solution ...
Jie Song 0001, Yubin Bao
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On 2-partition dimension of rotationally-symmetric graphs

Discrete Mathematics, Algorithms and Applications, 2022
The [Formula: see text]-partition dimension of graphs was introduced as generalization of partition dimension of graphs by Estrado–Moreno in 2020. Its applications can be seen in several areas including robot navigation, network designing, image processing and chemistry. Rotationally symmetric graphs are important in computer network topologies due to
Asim Nadeem, Agha Kashif, Sohail Zafar, Zohaib Zahid   +3 more
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The partition dimension of Cayley digraphs

Aequationes Mathematicae, 2006
Let G be a (di)graph and S a set of vertices of G. We say S resolves two vertices u and v of G if d(u, S) ≠ d(v, S). A partition $$ \prod $$ = {P1, P2,..., P k } of V (G) is a resolving partition of G if ...
Shonda Gosselin, Ortrud R Oellermann
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Partition dimension of rooted product graphs

Discrete Applied Mathematics, 2019
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Mohan Chris Monica, Samivel Santhakumar
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