Geodesic
The orderings of bicyclic graphs and connected graphs by algebraic connectivity
The electronic journal of combinatorics, Tome 17 (2010)
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The algebraic connectivity of a graph $G$ is the second smallest eigenvalue of its Laplacian matrix. Let $\mathscr{B}_n$ be the set of all bicyclic graphs of order $n$. In this paper, we determine the last four bicyclic graphs (according to their smallest algebraic connectivities) among all graphs in $\mathscr{B}_n$ when $n\geq 13$. This result, together with our previous results on trees and unicyclic graphs, can be used to further determine the last sixteen graphs among all connected graphs of order $n$. This extends the results of Shao et al. [The ordering of trees and connected graphs by their algebraic connectivity, Linear Algebra Appl. 428 (2008) 1421-1438].
DOI : 10.37236/434
Classification : 05C50, 05C38
Mots-clés : bicyclic graph, connected graph, algebraic connectivity, order 
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     author = {Jianxi Li and Ji-Ming Guo and Wai Chee Shiu},
     title = {The orderings of bicyclic graphs and connected graphs by algebraic connectivity},
     journal = {The electronic journal of combinatorics},
     year = {2010},
     volume = {17},
     doi = {10.37236/434},
     zbl = {1204.05056},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/434/}
}
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Jianxi Li; Ji-Ming Guo; Wai Chee Shiu. The orderings of bicyclic graphs and connected graphs by algebraic connectivity. The electronic journal of combinatorics, Tome 17 (2010). doi: 10.37236/434

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