Fibonacci numbers and Lucas numbers in graphs

被引：14

作者：

Startek, Mariusz ^{[1
]}

Wloch, Andrzej ^{[1
]}

Wloch, Iwona ^{[1
]}

机构：

[1] Rzeszow Tech Univ, Fac Math & Appl Phys, PL-35959 Rzeszow, Poland

来源：

DISCRETE APPLIED MATHEMATICS | 2009年 / 157卷 / 04期

关键词：

Independent sets; Fibonacci numbers; Counting; INDEPENDENT SETS; TREES;

D O I：

10.1016/j.dam.2008.08.028

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A subset S C V(G) is independent if no two vertices of S are adjacent in G. In this paper we study the number of independent sets in graphs with two elementary cycles. In particular we determine the smallest number and the largest number of these sets among n-vertex graphs with two elementary cycles. The extremal values of the number of independent sets are described using Fibonacci numbers and Lucas numbers. (C) 2008 Elsevier B.V. All rights reserved.

引用

页码：864 / 868

页数：5

共 50 条

[31] Complex factorizations of the Fibonacci and Lucas numbers
Cahill, ND
D'Errico, JR
Spence, JP
FIBONACCI QUARTERLY, 2003, 41 (01): : 13 - 19
[32] TRIGONOMETRIC EXPRESSIONS FOR FIBONACCI AND LUCAS NUMBERS
Sury, B.
ACTA MATHEMATICA UNIVERSITATIS COMENIANAE, 2010, 79 (02): : 199 - 208
[33] INTRA RATIOS OF FIBONACCI AND LUCAS NUMBERS
Choi, Eunmi
JP JOURNAL OF ALGEBRA NUMBER THEORY AND APPLICATIONS, 2015, 36 (01): : 43 - 62
[34] AN IDENTITY FOR THE FIBONACCI AND LUCAS-NUMBERS
JENNINGS, D
GLASGOW MATHEMATICAL JOURNAL, 1993, 35 : 381 - 384
[35] Fibonacci numbers, Lucas numbers and integrals of certain Gaussian processes
Baringhaus, L
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1996, 124 (12) : 3875 - 3884
[36] THE ORDER OF THE FIBONACCI AND LUCAS-NUMBERS
LENGYEL, T
FIBONACCI QUARTERLY, 1995, 33 (03): : 234 - 239
[37] FIBONACCI AND LUCAS NUMBERS AND COMPLEXITY OF A GRAPH
SHANNON, AG
FIBONACCI QUARTERLY, 1978, 16 (01): : 1 - 4
[38] Some identities for the generalized Fibonacci numbers and the generalized Lucas numbers
Wloch, Andrzej
APPLIED MATHEMATICS AND COMPUTATION, 2013, 219 (10) : 5564 - 5568
[39] FACTORIZATION OF FIBONACCI NUMBERS INTO PRODUCTS OF LUCAS NUMBERS AND RELATED RESULTS
Pongsriiam, Prapanpong
JP JOURNAL OF ALGEBRA NUMBER THEORY AND APPLICATIONS, 2016, 38 (04): : 363 - 372
[40] Properties of a class of numbers related to the Fibonacci, Lucas and Pell numbers
Dannan, FM
PROCEEDINGS OF THE SIXTH INTERNATIONAL CONFERENCE ON DIFFERENCE EQUATIONS: NEW PROGRESS IN DIFFERENCE EQUATIONS, 2004, : 399 - 406

← 1 2 3 4 5 →