Trees with a given number of leaves and the maximal number of maximum independent sets-Reference-Cited by-同舟云学术

Trees with a given number of leaves and the maximal number of maximum independent sets

Published:2021-04-01 Issue:2 Volume:31 Page:135-144
ISSN:1569-3929
Container-title:Discrete Mathematics and Applications
language:en
Short-container-title:

Author:

Taletskii Dmitriy S.¹,Malyshev Dmitriy S.²

Affiliation:

1. Lobachevsky State University of Nizhny Novgorod Nizhny Novgorod Russia

2. National Research University Higher School of Economics Moscow , Russia

Abstract

Abstract A complete description of trees with maximal possible number of maximum independent sets among all n-vertex trees with exactly l leaves is obtained. For all values of the parameters n and l the extremal tree is unique and is the result of merging the endpoints of l simple paths.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Discrete Mathematics and Combinatorics

Link

https://www.degruyter.com/document/doi/10.1515/dma-2021-0012/pdf

Reference20 articles.

1. Taletskii D. S., Malyshev D. S., “On trees of bounded degree with maximal number of greatest independent sets”, J. Appl. Industr. Math., 12:2 (2018), 369–381.

2. Taletskii D. S., Malyshev D. S., “Trees without twin-leaves with smallest number of maximal independent sets”, Discrete Math. Appl., 30:1 (2020), 53–67.

3. Aimei Y., Xuezheng L., “The Merrifield–Simmons indices and Hosoya indices of trees with k pendant vertices”, J. Math. Chem., 41:1 (2007), 33–43.

4. Chen Y.,Wen S., “On the total number of matchings of trees with prescribed diameter”, Int. J. Nonlin. Sci., 4:1 (2007), 37–43.

5. Dainyak A. B., “On the number of independent sets in the trees of a fixed diameter”, J. Appl. Industr.Math., 4:2 (2010), 163–171.