Lucas Sayılarıyla İlişkili İki Parçalı Graflar

Year 2020, Volume: 13 Issue: 3, 1069 - 1076, 31.12.2020

Ahmet Öteleş Diyar Omar Mustafa Zangana

https://doi.org/10.18185/erzifbed.712298

Abstract

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.

Keywords

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

Bipartite Graphs Associated with Lucas Numbers

Abstract

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.

Keywords

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

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