Journal ArticleDOI
Spectra of graph operations based on R-graph
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In this article, the adjacency spectra of four types of graph operations on and involving the R-graph of a regular graph and an arbitrary graph were determined for each edge of the regular graph by adding a new vertex for each vertex and joining each new vertex to the end vertices of the corresponding edge.Abstract:
For a regular graph and an arbitrary graph , we determine the adjacency (respectively, Laplacian and signless Laplacian) spectra of four types of graph operations on and involving the R-graph of , obtained from by adding a new vertex for each edge of and joining each new vertex to the end vertices of the corresponding edge. These results are then used to construct infinitely many pairs of adjacency (respectively, Laplacian and signless Laplacian) cospectral graphs.read more
Citations
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Book ChapterDOI
An Introduction to the Theory of Graph Spectra: Spectral techniques
TL;DR: In this article, the authors introduce the concept of graph operations and modifications, and characterizations of spectra by characterizations by spectra and one eigenvalue, and Laplacians.
An Introduction To The Theory Of Graph Spectra
TL;DR: An introduction to the theory of graph spectra is available in the book collection an online access to it is set as public so you can download it instantly and is universally compatible with any devices to read.
Journal ArticleDOI
Resistance distance and Kirchhoff index of R -vertex join and R -edge join of two graphs
TL;DR: The resistance distances and the Kirchhoff index of G 1 { v } G 2 and G 1{ e} G 2 respectively are formulated.
Journal ArticleDOI
Bounds for the general sum-connectivity index of composite graphs.
TL;DR: The lower and upper bounds for the general sum-connectivity index of four types of graph operations involving R-graph are obtained and the bounds of line graph L(X)$L( X)$ and rooted product of graphs are determined.
Journal ArticleDOI
On the Laplacian spectra of some variants of corona
Sasmita Barik,Gopinath Sahoo +1 more
TL;DR: In this paper, the spectral properties of super corona matrices and super neighbourhood corona matrix have been studied and all the eigenvalues and corresponding eigenvectors of these matrices have been described.
References
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BookDOI
Spectra of graphs
TL;DR: This book gives an elementary treatment of the basic material about graph Spectra, both for ordinary, and Laplace and Seidel spectra, by covering standard topics before presenting some new material on trees, strongly regular graphs, two-graphs, association schemes, p-ranks of configurations and similar topics.
Book
Spectra of graphs : theory and application
TL;DR: The Spectrum and the Group of Automorphisms as discussed by the authors have been used extensively in Graph Spectra Techniques in Graph Theory and Combinatory Applications in Chemistry an Physics. But they have not yet been applied to Graph Spectral Biblgraphy.
BookDOI
The Schur complement and its applications
TL;DR: Schur complements in statistics and probability have been used in Numerical Analysis as mentioned in this paper, where the Schur Complement has been applied in statistical and probability analysis. But their application is limited to statistical analysis.
Book
An Introduction to the Theory of Graph Spectra
TL;DR: In this article, the authors explore the theory of graph spectra, a topic with applications across a wide range of subjects, including computer science, quantum chemistry, electrical engineering and electrical engineering.
Book ChapterDOI
An Introduction to the Theory of Graph Spectra: Spectral techniques
TL;DR: In this article, the authors introduce the concept of graph operations and modifications, and characterizations of spectra by characterizations by spectra and one eigenvalue, and Laplacians.