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arXiv · 1407.5255

Laplacian spectral characterization of dumbbell graphs and theta graphs

Xiaogang Liu·Pengli Lu
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Abstract

Let $P_n$ and $C_n$ denote the path and cycle on $n$ vertices respectively. The dumbbell graph, denoted by $D_{p,k,q}$, is the graph obtained from two cycles $C_p$, $C_q$ and a path $P_{k+2}$ by identifying each pendant vertex of $P_{k+2}$ with a vertex of a cycle respectively. The theta graph, denoted by $Θ_{r,s,t}$, is the graph formed by joining two given vertices via three disjoint paths $P_{r}$, $P_{s}$ and $P_{t}$ respectively. In this paper, we prove that all dumbbell graphs as well as theta graphs are determined by their Laplacian spectra.

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Xiaogang Liu, Pengli Lu. 2014-08-11. Laplacian spectral characterization of dumbbell graphs and theta graphs. https://doi.org/10.1142/s1793830916500282

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