| Title:
|
A spectral bound for graph irregularity (English) |
| Author:
|
Goldberg, Felix |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
65 |
| Issue:
|
2 |
| Year:
|
2015 |
| Pages:
|
375-379 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The imbalance of an edge $e=\{u,v\}$ in a graph is defined as $i(e)=|d(u)-d(v)|$, where $d(\cdot )$ is the vertex degree. The irregularity $I(G)$ of $G$ is then defined as the sum of imbalances over all edges of $G$. This concept was introduced by Albertson who proved that $I(G) \leq 4n^{3}/27$ (where $n=|V(G)|$) and obtained stronger bounds for bipartite and triangle-free graphs. Since then a number of additional bounds were given by various authors. In this paper we prove a new upper bound, which improves a bound found by Zhou and Luo in 2008. Our bound involves the Laplacian spectral radius $\lambda $. (English) |
| Keyword:
|
irregularity |
| Keyword:
|
Laplacian matrix |
| Keyword:
|
degree |
| Keyword:
|
Laplacian index |
| MSC:
|
05C07 |
| MSC:
|
05C35 |
| MSC:
|
05C50 |
| idZBL:
|
Zbl 06486953 |
| idMR:
|
MR3360433 |
| DOI:
|
10.1007/s10587-015-0182-5 |
| . |
| Date available:
|
2015-06-16T17:45:09Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144276 |
| . |
| 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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| 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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| . |
