Taiwanese Journal of Mathematics

THE SECOND LARGEST NUMBER OF MAXIMAL INDEPENDENT SETS IN GRAPHS WITH AT MOST k CYCLES

Zemin Jin and Sherry H. F. Yan

Full-text: Open access

Abstract

Let $G$ be a simple undirected graph. Denote by $\mbox{ mi}(G)$ (respectively, $\mbox{xi}(G)$) the number of maximal (respectively, maximum) independent sets in $G$. In this paper we determine the second largest value of $\mbox{mi}(G)$ for graphs with at most $k$ cycles. Extremal graphs achieving these values are also determined.

Article information

Source
Taiwanese J. Math., Volume 13, Number 5 (2009), 1397-1410.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500405548

Digital Object Identifier
doi:10.11650/twjm/1500405548

Mathematical Reviews number (MathSciNet)
MR2554465

Zentralblatt MATH identifier
1206.05053

Subjects
Primary: 05C35: Extremal problems [See also 90C35] 05C69: Dominating sets, independent sets, cliques 68R10: Graph theory (including graph drawing) [See also 05Cxx, 90B10, 90B35, 90C35]

Keywords
maximal independent sets extremal graphs

Citation

Jin, Zemin; Yan, Sherry H. F. THE SECOND LARGEST NUMBER OF MAXIMAL INDEPENDENT SETS IN GRAPHS WITH AT MOST k CYCLES. Taiwanese J. Math. 13 (2009), no. 5, 1397--1410. doi:10.11650/twjm/1500405548. https://projecteuclid.org/euclid.twjm/1500405548


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