5×5 AT ÇİZGESİ İÇİN MODÜLERLİK İLE AT İLİŞKİLERİ TANIMI

Modülerlik çok kullanılan çizge analiz tekniğidir. Modülerlik belirtilen ağı anlamlı ilişkili gruplara ayırır. Gruplar aynı gruptaki düğümler arasındaki ortak özelliklerin varlığını belirtir. Bu çalışmada 5 At Kaplama Problemi (5-AKP) çözüm arayışında 5×5 at çizgesi modülerlik ile analiz ediyoruz. Araştırmamız çözünürlüğün 0.1 ile 1.8 olduğu aralık için tamamlandı. Maksimum modülerlik puanı 0.8 çözünürlüğü için 0.3 bulundu. Buna ek olarak 0.1 5-AKP’nin bazı çözümlerini bulmak için ideal çözünürlüktür. Ayrıca, analizler 1.0 çözünürlüğünün 5-AKP’nin çözümleri bulmak için en optimize çözünürlük olduğunu gösterdi. Son olarak modülerlik 172 çözümden 1’den 7’ye kadar tanımlayabilmektedir.

Anahtar Kelimeler:

At çizgesi, modülerlik, 5-AKP

IDENTIFICATION OF KNIGHTS’ RELATIONS FOR 5×5 KNIGHT GRAPH BY MODULARITY

Modularity is a widely utilized technic to analyze graphs. The modularity divides the specified network into relational clusters. The clusters highlight the shared properties between the clustered nodes. In the present study, we analyze 5×5 knight graph by modularity to extract 5 Knight Covering Problem (5-KCP) solutions. Our investigation is completed for resolutions from 0.1 to 1.8. The maximum modularity score is 0.3 found for resolution 0.8. Moreover, resolution 0.1 is the best resolution to find more solutions of 5-KCP. Also, the analyses show resolution 1.0 is the best resolution to find the solutions of 5-KCP efficiently. Lastly, modularity extracts the solutions from 1 to 7 out of 172 solutions.

Keywords:

Knight graph, Modularity, 5-KCP,

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