Pith. Sign in

RECORD

A switching method for constructing cospectral gain graphs

PaperPDF from arXiv

data files

Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
X Bluesky LinkedIn Reddit Hacker News
Aida Abiad, Francesco Belardo, Antonina P. Khramova

Combinatorics · Submitted 7 Apr 2023

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

The authors' main claim In this work, we show a new switching method to construct cospectral gain graphs.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗
Cite ▾
arXiv ID2304.03555 (version 1)
Pith IDTUHPONAM, Pith's permanent record of this paper and its review
CitationAida Abiad, Antonina P. Khramova, Francesco Belardo. "A switching method for constructing cospectral gain graphs." arXiv:2304.03555 (2023). https://pith.science/paper/TUHPONAM
Claim paper

The compiled record

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.

Open the compiled record

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,565 input tokens.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.05 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.02 · states quantitative result 0.03 · compares with prior results 0.86 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

A gain graph over a group $G$, also referred to as $G$-gain graph, is a graph where an element of a group $G$, called gain, is assigned to each oriented edge, in such a way that the inverse element is associated with the opposite orientation. Gain graphs can be regarded as a generalization of signed graphs, among others. In this work, we show a new switching method to construct cospectral gain graphs. Some previous methods known for graph cospectrality follow as a corollary of our results.

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 A gain graph over a group $G$, also referred to as $G$-gain graph, is a graph where an element of a group $G$, called gain, is assigned to each oriented edge, in such a way that the inverse element is associated with the opposite orientation. background 1.00 0.05 0.03 asserted 1.00
s1 Gain graphs can be regarded as a generalization of signed graphs, among others. background 1.00 0.05 0.02 asserted 0.93
s2 In this work, we show a new switching method to construct cospectral gain graphs. contribution 1.00 0.96 0.84 asserted 1.00
s3 Some previous methods known for graph cospectrality follow as a corollary of our results. interpretation 0.69 0.67 0.15 asserted 0.98

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

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • 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

A gain graph over a group $G$, also referred to as $G$-gain graph, is a graph where an element of a group $G$, called gain, is assigned to each oriented edge, in such a way that the inverse element is associated with the opposite orientation. Gain graphs can be regarded as a generalization of signed graphs, among others. In this work, we show a new switching method to construct cospectral gain graphs. Some previous methods known for graph cospectrality follow as a corollary of our results.

Human review

How Pith checks papers → · Full audit of this paper →

How the literature uses it

What this paper does with the arXiv papers it cites

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

What it cites · 6 sentences without a confident label

Builds on 1 paper
Uses the method or tool of 1 paper
Compares with 1 paper
  • It also cannot be constructed using the GM switching for $G$-cospectral graphs from [ref] since there is no suitable $G$-GM partition of $V_Γ$.

    Godsil-McKay switchings for gain graphs · A switching to construct $G$-cospectral gain graphs · 0.83

Cites as background 1 paper
  • In [ref] , the notion of $G$-cospectrality independent of the choice of $π$ was first introduced, and in [ref] , generalizations of GM-switching with respect to both $G$- and $π$-cospectrality were described.

    Godsil-McKay switchings for gain graphs · Concluding remarks · 0.93

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.