On generalized Pell numbers and their graph representations

• Autorzy: Włoch I.
• Języki publikacji: EN

Abstrakty

EN

In this paper we give a generalization of the Pell numbers and the Pell- Lucas numbers and next we apply this concept for their graph representations. We shall show that the generalized Pell numbers and the Pell-Lucas numbers are equal to the total number of k-independent sets in special graphs.

Słowa kluczowe

EN

Pell number; Pell-Lucas number; k-independent set of graph

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2008
• Tom: Vol. 48, [Z] 2
• Strony: 169--175
• Opis fizyczny: bibliogr. 10 poz.

Twórcy

autor

Włoch I.

• Rzeszow University of Technology, Faculty of Mathematics and Applied Physics ul.W.Pola 2,35-959 Rzeszów, Poland,

Bibliografia

• [1] S.B. Lin, C. Lin, Trees and forests with large and small independent indices, Chinese Journal of Mathematics, 23 (3) (1995) 199-210.
• [2] X. Lv, A. Yu, The Merrifield-Simmons Indices and Hosoya Indices of Trees with k Pendant Vertices, Journal of Mathematical Chemistry, Springer, 1 41 (2007) 33-43.
• [3] R.E. Merrifield, H.E. Simmons, Topological Methods in Chemistry, John Wiley & Sons, New York, 1989.
• [4] H. Prodinger, R.F. Tichy, Fibonacci numbers of graphs, The Fibonacci Quarterly 20 (1982) 16-21.
• [5] H.G. Sanchez, R. Gomez Alza, (k,l)-kernels, (k,l)-semikernels, k-Grundy functions and duality for state splittings, Discussiones Mathematicae Graph Theory 27(2) (2007), 359-373.
• [6] W. Szumny, A. W loch, I. W loch, On the existence and on the number of (k,l)-kernels in the lexicographic product of graphs, Discrete Mathematics, 308(2008), 4616-4624.
• [7] S. Wagner, Extremal trees with respect to Hosoya Index and Merrifield-Simmons Index, MATCH Communications in Mathematical and in Computer Chemistry, 57 (2007) 221-233.
• [8] E. Kilic, D. Tasci, The generalized Binet formula, reprezentation and sums of the generalized order-k Pell numbers, Taiwanese Journal of Mathematics, 10(6), (2006), 1661-1670.
• [9] M. Kwaśnik, I. W loch, The total number of generalized stable sets and kernels of graphs, Ars Combinatoria, 55 (2000), 139-146.
• [10] I. Włoch, Generalized Fibonacci polynomial of graph, Ars Combinatoria 68 (2003) 49-55.