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Record W2395208292

Broadcast domination of products of graphs.

2009· article· en· W2395208292 on OpenAlex
Boštjan Brešar, Simon Špacapan

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

venuePublished in a venue whose home country is Canada.
no affNo Canadian affiliation: this work is invisible to an affiliation-only frame.
No Canadian affiliation. An affiliation-only frame, the usual design, would never have seen this work. It is one of the works that make the case for inverting the frame.

Bibliographic record

VenueArs Combinatoria · 2009
Typearticle
Languageen
FieldComputer Science
TopicAdvanced Graph Theory Research
Canadian institutionsnot available
Fundersnot available
KeywordsMathematicsCartesian productDomination analysisCombinatoricsVertex (graph theory)Hamming graphUpper and lower boundsGraphDiscrete mathematicsHamming codeAlgorithm
DOInot available

Abstract

fetched live from OpenAlex

Broadcast domination in graphs is a variation of domination in which different integer weights are allowed on vertices and a vertex with weight k dominates its distance k-neighborhood. A distribution of weights on vertices of a graph G is called a dominating broadcast, if every vertex is dominated by some vertex with positive weight. The broadcast domination number γb(G) of a graph G is the minimum weight (the sum of weights over all vertices) of a dominating broadcast of G. In this paper we prove that for a connected graph G, γb(G) ≥ ⌈2rad(G)/3⌉. This general bound and a newly introduced concept of condensed dominating broadcast are used in obtaining sharp upper bounds for broadcast domination numbers of three standard graph products in terms of broadcast domination numbers of factors. A lower bound for a broadcast domination number of the Cartesian product of graphs is also determined, and graphs that attain it are characterized. Finally, as an application of these results we determine exact broadcast domination numbers of Hamming graphs and Cartesian products of cycles.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

Full frame distilled prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.

metaresearch head score (Codex)0.000
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.142
Threshold uncertainty score0.359

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.001
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0010.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.000

Machine scores (provisional)

The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.

Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.

Opus teacher head0.014
GPT teacher head0.274
Teacher spread0.260 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it