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k-Strong Shortest Path Union Cover for Certain Graphs and Networks

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Antony Xavier, Santiagu Theresal, Deepa Mathew, S. Arul Amirtha Raja

Combinatorics · Submitted 13 Apr 2021

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim 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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arXiv ID2104.05975 (version 1)
Pith IDFVHYXDN3, Pith's permanent record of this paper and its review
CitationAntony Xavier, Deepa Mathew, Santiagu Theresal, S. Arul Amirtha Raja. "k-Strong Shortest Path Union Cover for Certain Graphs and Networks." arXiv:2104.05975 (2021). https://pith.science/paper/FVHYXDN3
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,296 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.62 · human participants 0.02 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.23 · compares with prior results 0.06 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

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.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 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. background 1.00 0.14 0.04 asserted 0.99
s1 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. contribution 0.81 0.96 0.88 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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  • references and citing sentences
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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original 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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