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2013 CONNECTED GRAPHS WITH A LARGE NUMBER OF INDEPENDENT SETS
Min-Jen Jou
Taiwanese J. Math. 17(6): 2011-2017 (2013). DOI: 10.11650/tjm.17.2013.2309

Abstract

For a simple undirected graph $G=(V(G),E(G))$, a subset $I$ of $V(G)$ is said to be an independent set of $G$ if any two vertices in $I$ are not adjacent in $G$. An empty set is also an independent set in $G$. The set of all independent sets of a graph $G$ is denoted by $I(G)$ and its cardinality by $i(G)$ (known as the Merrifield-Simmons index in mathematical chemistry). Let $h(n,x)$ be the $x$-th largest number of independent sets among all connected $n$-vertex graphs. In this paper, we determine the numbers $h(n,x)$ for $1\le x\le \lfloor\frac{n}{2}\rfloor ^2-3\cdot\lfloor\frac{n}{2}\rfloor+3$. Besides, we also characterize the connected $n$-vertex graphs achieving these values.

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Min-Jen Jou. "CONNECTED GRAPHS WITH A LARGE NUMBER OF INDEPENDENT SETS." Taiwanese J. Math. 17 (6) 2011 - 2017, 2013. https://doi.org/10.11650/tjm.17.2013.2309

Information

Published: 2013
First available in Project Euclid: 10 July 2017

zbMATH: 1280.05102
MathSciNet: MR3141871
Digital Object Identifier: 10.11650/tjm.17.2013.2309

Subjects:
Primary: 05C30 , 05C69 , 68R10

Keywords: connected $n$-vertex graph , Independent set

Rights: Copyright © 2013 The Mathematical Society of the Republic of China

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Vol.17 • No. 6 • 2013
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