Combinatorics and Graph Theory

    

Characterizing Spectral Properties of Bridge Graphs

Authors: Yixin Li

Bridge graphs are special type of graphs which are constructed by connecting identical connected graphs with path graphs. We discuss different type of bridge graphs $B_{n\times l}^{m\times k}$ in this paper. In particular, we discuss the following: complete-type bridge graphs, star-type bridge graphs, and full binary tree bridge graphs. We also bound the second eigenvalues of the graph Laplacian of these graphs using methods from Spectral Graph Theory. In general, we prove that for general bridge graphs, $B_{n\times l}^2$, the second eigenvalue of the graph Laplacian should between $0$ and $2$, inclusive. At the end, we talk about the future work about infinite bridge graphs. We create definitions and found the related theorems to support our future work about infinite bridge graphs.

Comments: 34 Pages.

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Submission history

[v1] 2022-02-01 11:55:59

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