| Title:
|
Minimizing Laplacian spectral radius of unicyclic graphs with fixed girth (English) |
| Author:
|
Patra, Kamal Lochan |
| Author:
|
Sahoo, Binod Kumar |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
63 |
| Issue:
|
4 |
| Year:
|
2013 |
| Pages:
|
909-922 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we consider the following problem: Over the class of all simple connected unicyclic graphs on $n$ vertices with girth $g$ ($n$, $g$ being fixed), which graph minimizes the Laplacian spectral radius? Let $U_{n,g}$ be the lollipop graph obtained by appending a pendent vertex of a path on $n-g$ $(n> g)$ vertices to a vertex of a cycle on $g\geq 3$ vertices. We prove that the graph $U_{n,g}$ uniquely minimizes the Laplacian spectral radius for $n\geq 2g-1$ when $g$ is even and for $n\geq 3g-1$ when $g$ is odd. (English) |
| Keyword:
|
Laplacian matrix |
| Keyword:
|
Laplacian spectral radius |
| Keyword:
|
girth |
| Keyword:
|
unicyclic graph |
| MSC:
|
05C50 |
| idZBL:
|
Zbl 06373951 |
| idMR:
|
MR3165504 |
| DOI:
|
10.1007/s10587-013-0061-x |
| . |
| Date available:
|
2014-01-28T14:05:16Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143606 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| . |
