\(k\)-Lucas numbers and associated bipartite graphs
type: Item
instance of: scholarly article
title: \(k\)-Lucas numbers and associated bipartite graphs
zbMATH Open document ID: 0960.05079
DOI: 10.1016/S0024-3795(00)00204-4
published in: Linear Algebra and its Applications
publication date: 2001-05-10T00:00:00Z
review text: For a positive integer \(k\geq 2\), the \(k\)-Fibonacci sequence \(\{g_n^{(k)}\}\) is defined as: \(g_1^{(k)}=\dots=g_{k-2}^{(k)}=0\), \(g_{k-1}^{(k)}=g_k^{(k)}=1\) and for \(n>k\), \(g_n^{(k)}=g_{n-1}^{(k)}+g_{n-2}^{(k)}+\dots+g_{n-k}^{(k)}\). Moreover, the \(k\)th Lucas number is defined as \(l_n^{(k)}=g_{n-1}^{(k)}+g_{n+k-1}^{(k)}\) for \(n\geq 1\). The author constructs classes of bipartite graphs, whose numbers of \(1\)-factors are equal to \(k\)th Lucas number.
reviewed by: Martin Knor
Mathematics Subject Classification ID: 05C70
Mathematics Subject Classification ID: 11B39
zbMATH DE Number: 1556772
zbMATH Keywords: Fibonacci sequence
zbMATH Keywords: Lucas number
zbMATH Keywords: bipartite graphs
zbMATH Keywords: 1-factors
author: Gwangyeon Lee
MaRDI profile type: Publication
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Wikidata QID: Q128090184
description: scientific article; zbMATH DE number 1556772