## Journal of Applied Mathematics

### The Laplacian Spectral Radius of a Class of Unicyclic Graphs

Haixia Zhang

#### Abstract

Let $C\left(n,k\right)$ be the set of all unicyclic graphs with $n$ vertices and cycle length $k$. For any $U\in C\left(n,k\right)$, $U$ consists of the (unique) cycle (say ${C}_{k}$) of length $k$ and a certain number of trees attached to the vertices of ${C}_{k}$ having (in total) $n-k$ edges. If there are at most two trees attached to the vertices of ${C}_{k}$, where $k$ is even, we identify in the class of unicyclic graphs those graphs whose Laplacian spectral radii are minimal.

#### Article information

Source
J. Appl. Math., Volume 2013 (2013), Article ID 730396, 6 pages.

Dates
First available in Project Euclid: 14 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.jam/1394808305

Digital Object Identifier
doi:10.1155/2013/730396

Mathematical Reviews number (MathSciNet)
MR3145015

Zentralblatt MATH identifier
06950842

#### Citation

Zhang, Haixia. The Laplacian Spectral Radius of a Class of Unicyclic Graphs. J. Appl. Math. 2013 (2013), Article ID 730396, 6 pages. doi:10.1155/2013/730396. https://projecteuclid.org/euclid.jam/1394808305

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