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Journals / Avrupa Bilim ve Teknoloji Dergisi / 2026 / Sayı: 28 Özel Sayı

A Note On Bipartite Graphs with Domination Number 2 and 3

Baskınlık Sayısı 2 ve 3 Olan İki Parçalı Graflar Üzerine Bir Not

Havva Kırgız(SELCUK UNIVERSITY)0000-0003-0985-024X
Ayşe Dilek Maden(SELCUK UNIVERSITY)0000-0001-7717-0241
Pages
1071–1076
Publication Date
2021-11-30
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We also characterize the bipartite graphs which have the smallest MERD with the domination number 3.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:When each edge of a connected G graph is replaced by a unit resistor, the resistance distance is computed as the effective resistance between any two vertices in G.
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Key Findings & Data:In this paper, we characterize the bipartite graphs which have the smallest and largest MERD with domination number 2 are given.
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Conclusion & Impact:We also characterize the bipartite graphs which have the smallest MERD with the domination number 3.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Elektik devreleri · Kirchhoff indeks · İki parçalı graflar

Abstract

When each edge of a connected G graph is replaced by a unit resistor, the resistance distance is computed as the effective resistance between any two vertices in G. The Kirchhoff index of G is given by the sum of resistance distances between all pairs of vertices. The multiplicative eccentricity resistance-distance (MERD) of a connected graph G is defined as , where is the set of vertices of , is the resistance-distance between the vertices and , and are the eccentricity of the vertices and , respectively. The MERD of the G can be obtained by using Kirchhoff index. In this paper, we characterize the bipartite graphs which have the smallest and largest MERD with domination number 2 are given. We also characterize the bipartite graphs which have the smallest MERD with the domination number 3.

Özet

Bağlantılı bir G grafının tüm kenarları birim direnç ile değiştirildiğinde, direnç mesafesi G ’nin herhangi iki köşesi arasındaki efektif direnç olarak hesaplanır. ’nin Kirchhoff indeksi tüm köşe çiftlerinin direnç mesafelerinin toplamı olarak tanımlanır. , G ’nin köşelerinin kümesi, ise ile köşeleri arasındaki direnç mesafesi ve , de sırasıyla ve köşelerinin eksantriği olmak üzere, bağlantılı bir grafının çarpımsal eksantrik direnç mesafası (ÇEDM) olarak tanımlanır. G grafının ÇEDM’i Kirchhoff indeksini kullanarak hesaplanabilir. Bu makalede, baskınlık sayısı 2 olan iki parçalı graflardan en küçük ve en büyük ÇEDM’e sahip olanlar karakterize edilmiştir. Ayrıca baskınlık sayısı 3 olan iki parçalı graflardan en küçük ÇEDM’e sahip olanlar karakterize edilmiştir

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Cite This Article

Kırgız, H., Maden, A. D. (2021). A Note On Bipartite Graphs with Domination Number 2 and 3. Avrupa Bilim ve Teknoloji Dergisi, Sayı: 28 Özel Sayı, 1071–1076. https://doi.org/10.31590/ejosat.1012651

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