Pith. Sign in

RECORD

Sum and integral sum graphs -- A survey

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
Lowell W. Beineke, V. Vilfred Kamalappan

Combinatorics · Submitted 15 Jul 2024

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

The authors' main claim In this survey article, the authors bring out several properties of sum and integral sum graphs obtained by different authors.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗
Cite ▾
arXiv ID2407.10917 (version 1)
Pith IDKL75XMOJ, Pith's permanent record of this paper and its review
CitationLowell W. Beineke, V. Vilfred Kamalappan. "Sum and integral sum graphs -- A survey." arXiv:2407.10917 (2024). https://pith.science/paper/KL75XMOJ
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, 3,033 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.06 · human participants 0.02 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.06 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

Frank Harary introduced the concepts of sum and integral sum graphs. A graph $G$ is a \textit{sum graph} if the vertices of $G$ can be labeled with distinct positive integers so that $e = uv$ is an edge of $G$ if and only if the sum of the labels on vertices $u$ and $v$ is also a label in $G.$ An \textit{integral sum graph} is also defined just as sum graph, the difference being that the labels may be any distinct integers. In this survey article, the authors bring out several properties of sum and integral sum graphs obtained by different authors.

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 Frank Harary introduced the concepts of sum and integral sum graphs. background 1.00 0.03 0.03 asserted 1.00
s1 A graph $G$ is a \textit{sum graph} if the vertices of $G$ can be labeled with distinct positive integers so that $e = uv$ is an edge of $G$ if and only if the sum of the labels on vertices $u$ and $v$ is also a label in $G.$ An \textit{integral sum graph} is also defined just as sum graph, the difference being that the labels may be any distinct integers. background 1.00 0.05 0.05 asserted 1.00
s2 In this survey article, the authors bring out several properties of sum and integral sum graphs obtained by different authors. contribution 0.98 0.29 0.17 asserted 1.00

What kind of paper the classifier reports this is: review 1.00 · evidence from literature 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

Frank Harary introduced the concepts of sum and integral sum graphs. A graph $G$ is a \textit{sum graph} if the vertices of $G$ can be labeled with distinct positive integers so that $e = uv$ is an edge of $G$ if and only if the sum of the labels on vertices $u$ and $v$ is also a label in $G.$ An \textit{integral sum graph} is also defined just as sum graph, the difference being that the labels may be any distinct integers. In this survey article, the authors bring out several properties of sum and integral sum graphs obtained by different authors.

Human review

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

Discussion

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