Geodesic
The signless Laplacian spectral radius of unicyclic and bicyclic graphs with a given girth
The electronic journal of combinatorics, Tome 18 (2011) no. 1
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Let $\mathcal{U}(n,g)$ and $\mathcal{B}(n,g)$ be the set of unicyclic graphs and bicyclic graphs on $n$ vertices with girth $g$, respectively. Let $\mathcal{B}_{1}(n,g)$ be the subclass of $\mathcal{B}(n,g)$ consisting of all bicyclic graphs with two edge-disjoint cycles and $\mathcal{B}_{2}(n,g)=\mathcal{B}(n,g)\backslash\mathcal{B}_{1}(n,g)$. This paper determines the unique graph with the maximal signless Laplacian spectral radius among all graphs in $\mathcal{U}(n,g)$ and $\mathcal{B}(n,g)$, respectively. Furthermore, an upper bound of the signless Laplacian spectral radius and the extremal graph for $\mathcal{B}(n,g)$ are also given.
DOI : 10.37236/670
Classification : 05C50, 15A18
Mots-clés : Unicyclic graph, Bicyclic graph, Signless Laplacian matrix, Spectral radius, Girth 
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     author = {Ke Li and Ligong Wang and Guopeng Zhao},
     title = {The signless {Laplacian} spectral radius of unicyclic and bicyclic graphs with a given girth},
     journal = {The electronic journal of combinatorics},
     year = {2011},
     volume = {18},
     number = {1},
     doi = {10.37236/670},
     zbl = {1230.05200},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/670/}
}
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Ke Li; Ligong Wang; Guopeng Zhao. The signless Laplacian spectral radius of unicyclic and bicyclic graphs with a given girth. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/670

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