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Extremal Permanents of Laplacian Matrices of Unicyclic Graphs
The extremal problem of Laplacian permanents of graphs is a classical and challenging topic in algebraic combinatorics, where the inherent #P-complete complexity of permanent computation renders this pursuit particularly intractable.
Tingzeng Wu +2 more
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On the Second Largest Spectral Radius of Unicyclic Bipartite Graphs
Discrete Mathematics, Algorithms and Applications, 2011 In this paper, we determine the two graphs in the class of unicyclic bipartite graphs with n vertices, having the first two largest spectral radius.
Milan Nath
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On Invertible Non-Bipartite Unicyclic Graphs With a Unique Perfect Matching and Their Smallest Positive Eigenvalues [PDF]
Electronic Journal of Linear AlgebraLet $G$ be a simple connected graph with the adjacency matrix $A(G)$. By the smallest positive eigenvalue of $G$, we mean the smallest positive eigenvalue of $A(G)$ and denote it by $\tau(G)$.
Sasmita Barik, Debabrota Mondal
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Permanental Bounds for the Signless Laplacian Matrix of Bipartite Graphs and Unicyclic Graphs
Linear and Multilinear Algebra, 2011Shuchao Li
exaly
Ordering Non-Bipartite Unicyclic Graphs With Pendant Vertices by the Least Q-Eigenvalue
Journal of Inequalities and Applications, 2016Guanglong Yu, Shu-Guang Guo
exaly
On the Least Eigenvalue of a Unicyclic Mixed Graph
Linear and Multilinear Algebra, 2005Yi-Zheng Fan
exaly
First Eigenvalue and First Eigenvectors of a Nonsingular Unicyclic Mixed Graph
Discrete Mathematics, 2009Yi-Zheng Fan, Yu-Bin Gao
exaly
First Eigenvalue of Nonsingular Mixed Unicyclic Graphs With Fixed Number of Branch Vertices
Taiwanese Journal of Mathematics, 2016Bo Zhou
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