First eigenvalue and first eigenvectors of a nonsingular unicyclic mixed graph

DOI10.1016/j.disc.2008.05.034zbMath1182.05081OpenAlexW1978818194MaRDI QIDQ1025507

Yi-Zheng Fan, Yi Wang, Shi-Cai Gong, Yu-Bin Gao

Publication date: 19 June 2009

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.disc.2008.05.034

zbMATH Keywords

eigenvalueeigenvectorgirthunicyclic graphmixed graphcharacteristic set

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50)

Related Items (15)

Extremizing first eigenvalue of 3-colored digraphs made with given blocks ⋮ Unnamed Item ⋮ On the spectrum of some signed complete and complete bipartite graphs ⋮ The least eigenvalue of signless Laplacian of non-bipartite graphs with given domination number ⋮ Bipartiteness and the least eigenvalue of signless Laplacian of graphs ⋮ On the signless Laplacian index of cacti with a given number of pendant vertices ⋮ The least eigenvalue of signless Laplacian of graphs under perturbation ⋮ The least eigenvalue of the signless Laplacian of the complements of trees ⋮ Line star sets for Laplacian eigenvalues ⋮ On weighted directed graphs ⋮ Singularity of Hermitian (quasi-)Laplacian matrix of mixed graphs ⋮ The signless Laplacian or adjacency spectral radius of bicyclic graphs with given number of cut edges ⋮ Maximizing signless Laplacian or adjacency spectral radius of graphs subject to fixed connectivity ⋮ The second least eigenvalue of the signless Laplacian of the complements of trees ⋮ First eigenvalue of nonsingular mixed graphs with given number of pendant vertices

Cites Work

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• Laplacian matrices of graphs: A survey
• Algebraic graph theory without orientation
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• Minimizing algebraic connectivity over connected graphs with fixed girth
• The third smallest eigenvalue of the Laplacian matrix
• Characteristic vertices of weighted trees via perron values
• Generalized matrix tree theorem for mixed graphs
• Algebraic connectivity of weighted trees under perturbation
• Extremizing algebraic connectivity subject to graph theoretic constraints
• Maximizing Algebraic Connectivity Over Unicyclic Graphs
• Edge version of the matrix tree theorem for trees
• On the least eigenvalue of a unicyclic mixed graph
• Algebraic connectivity and the characteristic set of a graph
• Characteristic vertices of trees^*

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