The orderings of bicyclic graphs and connected graphs by algebraic connectivity

Jianxi Li; Ji Ming Guo; Wai Chee Shiu

doi:10.37236/434

The orderings of bicyclic graphs and connected graphs by algebraic connectivity

Jianxi Li^*, Ji Ming Guo, Wai Chee Shiu

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

5 Citations (Scopus)

Abstract

The algebraic connectivity of a graph G is the second smallest eigenvalue of its Laplacian matrix. Let 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 B_n when n ≥ 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.

Original language	English
Article number	R162
Number of pages	11
Journal	Electronic Journal of Combinatorics
Volume	17
Issue number	1
DOIs	https://doi.org/10.37236/434
Publication status	Published - 3 Dec 2010

Scopus Subject Areas

Theoretical Computer Science
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics
Applied Mathematics

User-Defined Keywords

Algebraic connectivity
Bicyclic graph
Connected graph
Order

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10.37236/434

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N2 - The algebraic connectivity of a graph G is the second smallest eigenvalue of its Laplacian matrix. Let Bn 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 Bn when n ≥ 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.

AB - The algebraic connectivity of a graph G is the second smallest eigenvalue of its Laplacian matrix. Let Bn 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 Bn when n ≥ 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.

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KW - Connected graph

KW - Order

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The orderings of bicyclic graphs and connected graphs by algebraic connectivity

Abstract

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