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Keywords = necklace graph

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9 pages, 437 KiB  
Article
Wirelength of Enhanced Hypercube into Windmill and Necklace Graphs
by Jia-Bao Liu, Micheal Arockiaraj and John Nancy Delaila
Mathematics 2019, 7(5), 383; https://doi.org/10.3390/math7050383 - 26 Apr 2019
Cited by 9 | Viewed by 3351
Abstract
An embedding of an interconnection network into another is one of the main issues in parallel processing and computing systems. Congestion, dilation, expansion and wirelength are some of the parameters used to analyze the efficiency of an embedding in which resolving the wirelength [...] Read more.
An embedding of an interconnection network into another is one of the main issues in parallel processing and computing systems. Congestion, dilation, expansion and wirelength are some of the parameters used to analyze the efficiency of an embedding in which resolving the wirelength problem reduces time and cost in the embedded design. Due to the potential topological properties of enhanced hypercube, it has become constructive in recent years, and a lot of research work has been carried out on it. In this paper, we use the edge isoperimetric problem to produce the exact wirelengths of embedding enhanced hypercube into windmill and necklace graphs. Full article
(This article belongs to the Special Issue Graph-Theoretic Problems and Their New Applications)
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10 pages, 297 KiB  
Article
Edge Version of Metric Dimension and Doubly Resolving Sets of the Necklace Graph
by Jia-Bao Liu, Zohaib Zahid, Ruby Nasir and Waqas Nazeer
Mathematics 2018, 6(11), 243; https://doi.org/10.3390/math6110243 - 7 Nov 2018
Cited by 40 | Viewed by 5064
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 of edge version of metric dimension and doubly [...] Read more.
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 of edge version of metric dimension and doubly resolving sets is based on the distances of edges in a graph. In this paper, we find the edge version of metric dimension and doubly resolving sets for the necklace graph. Full article
(This article belongs to the Special Issue Discrete Optimization: Theory, Algorithms, and Applications)
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