Preface 1. Introduction 2. Graph operations and modifications 3. Spectrum and structure 4. Characterizations by spectra 5. Structure and one eigenvalue 6. Spectral techniques 7. Laplacians 8. Additional topics 9. Applications Appendix Bibliography Index of symbols Index.

An Introduction to the Theory of Graph Spectra: Spectral techniques

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An Introduction To The Theory Of Graph Spectra

Resistance distance and Kirchhoff index of R -vertex join and R -edge join of two graphs

The general sum-connectivity index is a molecular descriptor defined as $\chi_{\alpha}(X)=\sum_{xy\in E(X)}(d_{X}(x)+d_{X}(y))^{\alpha}$
 , where $d_{X}(x)$
 denotes the degree of a vertex $x\in X$
 , and α is a real number. Let X be a graph; then let $R(X)$
 be the graph obtained from X by adding a new vertex $x_{e}$
 corresponding to each edge of X and joining $x_{e}$
 to the end vertices of the corresponding edge $e\in E(X)$
 . In this paper we obtain the lower and upper bounds for the general sum-connectivity index of four types of graph operations involving R-graph. Additionally, we determine the bounds for the general sum-connectivity index of line graph $L(X)$
 and rooted product of graphs.

/pdf/bounds-for-the-general-sum-connectivity-index-of-composite-15mboacrgy.pdf

Bounds for the general sum-connectivity index of composite graphs.

On the Laplacian spectra of some variants of corona

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.

Jie Lan

Papers

Spectra of graph operations based on R-graph