Spectral characterizations of dumbbell graphs
The electronic journal of combinatorics, Tome 17 (2010)
A dumbbell graph, denoted by $D_{a,b,c}$, is a bicyclic graph consisting of two vertex-disjoint cycles $C_a$, $C_b$ and a path $P_{c+3}$ ($c \geq -1$) joining them having only its end-vertices in common with the two cycles. In this paper, we study the spectral characterization w.r.t. the adjacency spectrum of $D_{a,b,0}$ (without cycles $C_4$) with $\gcd(a,b)\geq 3$, and we complete the research started in [J.F. Wang et al., A note on the spectral characterization of dumbbell graphs, Linear Algebra Appl. 431 (2009) 1707–1714]. In particular we show that $D_{a,b,0}$ with $3 \leq \gcd(a,b) < a$ or $\gcd(a,b)=a$ and $b\neq 3a$ is determined by the spectrum. For $b=3a$, we determine the unique graph cospectral with $D_{a,3a,0}$. Furthermore we give the spectral characterization w.r.t. the signless Laplacian spectrum of all dumbbell graphs.
@article{10_37236_314,
author = {Jianfeng Wang and Francesco Belardo and Qiongxiang Huang and Enzo M. Li Marzi},
title = {Spectral characterizations of dumbbell graphs},
journal = {The electronic journal of combinatorics},
year = {2010},
volume = {17},
doi = {10.37236/314},
zbl = {1215.05107},
url = {http://geodesic.mathdoc.fr/articles/10.37236/314/}
}
TY - JOUR AU - Jianfeng Wang AU - Francesco Belardo AU - Qiongxiang Huang AU - Enzo M. Li Marzi TI - Spectral characterizations of dumbbell graphs JO - The electronic journal of combinatorics PY - 2010 VL - 17 UR - http://geodesic.mathdoc.fr/articles/10.37236/314/ DO - 10.37236/314 ID - 10_37236_314 ER -
Jianfeng Wang; Francesco Belardo; Qiongxiang Huang; Enzo M. Li Marzi. Spectral characterizations of dumbbell graphs. The electronic journal of combinatorics, Tome 17 (2010). doi: 10.37236/314
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