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Strong domination number of a modified graph

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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Saeid Alikhani, Nima Ghanbari

Combinatorics · Submitted 4 Dec 2022

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

The authors' main claim In this paper, we study the effects on $\gamma_{st}(G)$ when $G$ is modified by operations on vertex and edge of $G$.

how it is stated · asserted 0.76 read the record →

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arXiv ID2212.01860 (version 1)
Pith IDA2TSZGSF, Pith's permanent record of this paper and its review
CitationNima Ghanbari, Saeid Alikhani. "Strong domination number of a modified graph." arXiv:2212.01860 (2022). https://pith.science/paper/A2TSZGSF
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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, 3,619 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.04 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.05 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

Let $G=(V,E)$ be a simple graph. A set $D\subseteq V$ is a strong dominating set of $G$, if for every vertex $x\in V\setminus D$ there is a vertex $y\in D$ with $xy\in E(G)$ and $deg(x)\leq deg(y)$. The strong domination number $\gamma_{st}(G)$ is defined as the minimum cardinality of a strong dominating set. In this paper, we study the effects on $\gamma_{st}(G)$ when $G$ is modified by operations on vertex and edge of $G$.

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 Let $G=(V,E)$ be a simple graph. background 1.00 0.04 0.01 asserted 0.73
s1 A set $D\subseteq V$ is a strong dominating set of $G$, if for every vertex $x\in V\setminus D$ there is a vertex $y\in D$ with $xy\in E(G)$ and $deg(x)\leq deg(y)$. background 1.00 0.05 0.02 asserted 0.99
s2 The strong domination number $\gamma_{st}(G)$ is defined as the minimum cardinality of a strong dominating set. background 1.00 0.08 0.03 asserted 1.00
s3 In this paper, we study the effects on $\gamma_{st}(G)$ when $G$ is modified by operations on vertex and edge of $G$. contribution 1.00 0.75 0.08 asserted 0.76

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.99.

What was examined, and what was not

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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

Let $G=(V,E)$ be a simple graph. A set $D\subseteq V$ is a strong dominating set of $G$, if for every vertex $x\in V\setminus D$ there is a vertex $y\in D$ with $xy\in E(G)$ and $deg(x)\leq deg(y)$. The strong domination number $\gamma_{st}(G)$ is defined as the minimum cardinality of a strong dominating set. In this paper, we study the effects on $\gamma_{st}(G)$ when $G$ is modified by operations on vertex and edge of $G$.

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