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On the maximum number of maximum independent sets in connected graphs
- Publication Year :
- 2018
-
Abstract
- We characterize the connected graphs of given order $n$ and given independence number $\alpha$ that maximize the number of maximum independent sets. For $3\leq \alpha\leq n/2$, there is a unique such graph that arises from the disjoint union of $\alpha$ cliques of orders $\left\lceil\frac{n}{\alpha}\right\rceil$ and $\left\lfloor\frac{n}{\alpha}\right\rfloor$, by selecting a vertex $x$ in a largest clique and adding an edge between $x$ and a vertex in each of the remaining $\alpha-1$ cliques. Our result confirms a conjecture of Derikvand and Oboudi [On the number of maximum independent sets of graphs, Transactions on Combinatorics 3 (2014) 29-36].
- Subjects :
- Mathematics - Combinatorics
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1806.10424
- Document Type :
- Working Paper