Lucas Sayılarıyla İlişkili İki Parçalı Graflar

Öz

Bu çalışmada iki parçalı komşuluk matrisi n×n mertebeli (0,1)-circulant matrisi olan iki parçalı bir graf ele aldık. Daha sonra bu grafın mükemmel eşlemelerinin (1-factor) sayılarının Lucas sayıları ile arasındaki ilişkiyi verdik. Son olarak da bu mükemmel eşlemelerin sayısını hesaplamak için bazı maple prosedürleri verdik.

Anahtar Kelimeler

• Mükemmel eşleme
• İki parçalı graf
• Permanent
• Fibonacci sayısı
• Lucas sayısı

Bipartite Graphs Associated with Lucas Numbers

Öz

In this paper, we consider the bipartite graph whose bipartite adjacency matrix is an n×n (0,1)-circulant matrix. Then we show that the numbers of perfect matchings of this graph are equal to the well-known Lucas numbers. Finally, we give some Maple procedures in order to calculate the numbers of perfect matchings of the bipartite graph.

Anahtar Kelimeler

• Fibonacci number,
• Lucas number
• Perfect matching
• bipartite graph
• permanent,

Kaynakça

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