Note: Fibonacci numbers and Lucas numbers in graphs

Authors:
Mariusz Startek;Andrzej Włoch;Iwona Włoch
Affiliations:
Technical University of Rzeszów, Faculty of Mathematics and Applied Physics, ul.W.Pola 2, 35-959 Rzeszów, Poland;Technical University of Rzeszów, Faculty of Mathematics and Applied Physics, ul.W.Pola 2, 35-959 Rzeszów, Poland;Technical University of Rzeszów, Faculty of Mathematics and Applied Physics, ul.W.Pola 2, 35-959 Rzeszów, Poland
Venue:
Discrete Applied Mathematics
Year:
2009

Citing 1
Cited 2

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Abstract

A subset S@?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.