Algebraic conditions for -tough graphs
We give some algebraic conditions for -tough graphs in terms of the Laplacian eigenvalues and adjacency eigenvalues of graphs.
Algebraic connectivity of -connected graphs
Let be a -connected graph with . A hinge is a subset of vertices whose deletion from yields a disconnected graph. We consider the algebraic connectivity and Fiedler vectors of such graphs, paying special attention to the signs of the entries in Fiedler vectors corresponding to vertices in a hinge, and to vertices in the connected components at a hinge. The results extend those in Fiedler’s papers Algebraic connectivity of graphs (1973), A property of eigenvectors of nonnegative symmetric...
Algebraic connectivity of trees
Algebraic connectivity of trees with a pendant edge of infinite weight.
Algebraic Structure Count of Some Cyclic Hexagonal-square Chains
Algorithms 62-64. Graph-theoretic algorithms for sparse matrix transformations
All graphs in which each pair of distinct vertices has exactly two common neighbors
We find all connected graphs in which any two distinct vertices have exactly two common neighbors, thus solving a problem by B. Zelinka.
An eigenvalue characterization of antipodal distance-regular graphs.
An identity between the determinant and the permanent of Hessenberg-type matrices
In this short note we provide an extension of the notion of Hessenberg matrix and observe an identity between the determinant and the permanent of such matrices. The celebrated identity due to Gibson involving Hessenberg matrices is consequently generalized.
An upper bound on algebraic connectivity of graphs with many cutpoints.
An upper bound on the Laplacian spectral radius of the signed graphs
In this paper, we established a connection between the Laplacian eigenvalues of a signed graph and those of a mixed graph, gave a new upper bound for the largest Laplacian eigenvalue of a signed graph and characterized the extremal graph whose largest Laplacian eigenvalue achieved the upper bound. In addition, an example showed that the upper bound is the best in known upper bounds for some cases.
Analyse hiérarchique des préférences et généralisations de la transitivité
Another class of equienergetic graphs
Applications of Graph Spectra: an Introduction to the Literature
Applications of Graph Spectra: An Introduction to the Literature
Applications of Graph Spectra in Quantum Physics
Applications of Shortest Path Algorithms to Matrix Scalings.
Approximating the isoperimetric number of strongly regular graphs.
Asymptotic spectral analysis of generalized Erdős-Rényi random graphs
Motivated by the Watts-Strogatz model for a complex network, we introduce a generalization of the Erdős-Rényi random graph. We derive a combinatorial formula for the moment sequence of its spectral distribution in the sparse limit.
Asymptotic spectral analysis of growing graphs: odd graphs and spidernets
Two new examples are given for illustrating the method of quantum decomposition in the asymptotic spectral analysis for a growing family of graphs. The odd graphs form a growing family of distance-regular graphs and the two-sided Rayleigh distribution appears in the limit of vacuum spectral distribution of the adjacency matrix. For a spidernet as well as for a growing family of spidernets the vacuum distribution of the adjacency matrix is the free Meixner law. These distributions are calculated...