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Maximum zeroth-order general Randi\'{c} index of orientations of trees, unicyclic and bicyclic graphs with given matching number

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Jiaxiang Yang, Hanyuan Deng

Combinatorics · Submitted 10 Dec 2021

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

The authors' main claim We determine maximum zeroth-order general Randi\'{c} index of oriented trees, unicyclic and bicyclic graphs in terms of matching number and order in this paper.

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arXiv ID2112.05378 (version 3)
Pith IDP7IM7Z56, Pith's permanent record of this paper and its review
CitationHanyuan Deng, Jiaxiang Yang. "Maximum zeroth-order general Randi\'{c} index of orientations of trees, unicyclic and bicyclic graphs with given matching number." arXiv:2112.05378 (2021). https://pith.science/paper/P7IM7Z56
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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, 2,518 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.06 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.32 · compares with prior results 0.05 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; .

The zeroth-order general Randi\'{c} index $R^{0}_{a}$ of a digraph $D$ is the sum of $(d^{+}_{v})^{a}+(d^{-}_{w})^{a}$ over all arcs $vw$ of $D$, where $a$, $d^{+}_{v}$ and $d^{-}_{w}$ are an arbitrary real number, the out-degree of the vertex $v$ and the in-degree of the vertex $w$, respectively. We determine maximum zeroth-order general Randi\'{c} index of oriented trees, unicyclic and bicyclic graphs in terms of matching number and order in this paper.

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 zeroth-order general Randi\'{c} index $R^{0}_{a}$ of a digraph $D$ is the sum of $(d^{+}_{v})^{a}+(d^{-}_{w})^{a}$ over all arcs $vw$ of $D$, where $a$, $d^{+}_{v}$ and $d^{-}_{w}$ are an arbitrary real number, the out-degree of the vertex $v$ and the in-degree of the vertex $w$, respectively. background 1.00 0.08 0.02 asserted 0.99
s1 We determine maximum zeroth-order general Randi\'{c} index of oriented trees, unicyclic and bicyclic graphs in terms of matching number and order in this paper. contribution 0.84 0.96 0.93 asserted 1.00

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

What was examined, and what was not

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not examined
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  • references and citing sentences
  • relations to other papers
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  • P abstract
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  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

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 zeroth-order general Randi\'{c} index $R^{0}_{a}$ of a digraph $D$ is the sum of $(d^{+}_{v})^{a}+(d^{-}_{w})^{a}$ over all arcs $vw$ of $D$, where $a$, $d^{+}_{v}$ and $d^{-}_{w}$ are an arbitrary real number, the out-degree of the vertex $v$ and the in-degree of the vertex $w$, respectively. We determine maximum zeroth-order general Randi\'{c} index of oriented trees, unicyclic and bicyclic graphs in terms of matching number and order in this paper.

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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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