k-Strong Shortest Path Union Cover for Certain Graphs and Networks
Antony Xavier, Santiagu Theresal, Deepa Mathew, S. Arul Amirtha Raja
TL;DR
This paper investigates the k-strong shortest path union cover problem, determining exact solutions for specific graphs and proving its NP-completeness in general, highlighting computational complexity challenges.
Contribution
It provides exact solutions for the 2-strong cover in certain graphs and establishes the NP-completeness of the general problem.
Findings
Exact 2-strong covers for specific graphs
Proof of NP-completeness for the general problem
Complexity results for k-strong shortest path union cover
Abstract
The k-distance strong shortest path union cover of a graph is the minimum cardinality among all strong shortest path union cover at distance k of G. In this paper we determine the 2-strong shortest path union cover for certain graphs, also we prove that the k-strong shortest path union cover problem, in general, is NP-complete.
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Taxonomy
TopicsInterconnection Networks and Systems · Advanced Graph Theory Research · VLSI and FPGA Design Techniques