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

Zemin Jin, 金澤民, Sherry H. F. Yan and 嚴慧芳
Taiwanese Journal of Mathematics
Vol. 13, No. 5 (October 2009), pp. 1397-1410
Stable URL: http://www.jstor.org/stable/43833417
Page Count: 14
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
THE SECOND LARGEST NUMBER OF MAXIMAL INDEPENDENT SETS IN GRAPHS WITH AT MOST k CYCLES
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Abstract

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

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