Fibonacci numbers in graphs with strong (1, 1, 2)-kernels-Reference-Cited by-同舟云学术

Fibonacci numbers in graphs with strong (1, 1, 2)-kernels

Published:2021-02-23 Issue:1 Volume:27 Page:
ISSN:1405-213X
Container-title:Boletín de la Sociedad Matemática Mexicana
language:en
Short-container-title:Bol. Soc. Mat. Mex.

Author:

Bednarz Urszula^ORCID,Włoch Iwona

Abstract

AbstractIn this paper, we study strong (1, 1, 2)-kernels in graphs which generalize classical kernels, (1, 2)-kernels and 2-dominating kernels, simultaneously. We give a complete characterization of trees with a strong (1, 1, 2)-kernel. Moreover, we present some realization theorems and show connections between the number of strong (1, 1, 2)-kernels and Fibonacci and Lucas numbers.

Publisher

Springer Science and Business Media LLC

Subject

General Mathematics

Link

http://link.springer.com/content/pdf/10.1007/s40590-021-00328-0.pdf

Reference25 articles.

1. Bednarz, P., Hernandez-Cruz, C., Włoch, I.: On the existence and number of (2-d)-kernels in graphs. Ars Comb. 121, 341–351 (2015)

2. Bednarz, P., Włoch, I.: On (2-d)-kernels in the cartesian product of graphs. Ann. UMCS Sec. A 70(2), 1–8 (2016)

3. Bednarz, P., Włoch, I.: An algorithm determining (2-d)-kernels in trees. Util. Math. 102, 215–222 (2017)

4. Bednarz, U.: Strong (1,1,2)-kernels in the corona of graphs and some realization problems. Iran. J. Sci. Technol. A 44, 401–406 (2020)

5. Bednarz, U., Włoch, I.: On strong (1,1,2)-kernels in graphs. Ars Comb. (in press)

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