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A note on the spectral characterization of dumbbell graphs

✍ Scribed by Jianfeng Wang; Qiongxiang Huang; Francesco Belardo; Enzo M. Li Marzi

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
160 KB
Volume
431
Category
Article
ISSN
0024-3795

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✦ Synopsis

The dumbbell graph, denoted by D a,b,c , is a bicyclic graph consisting of two vertex-disjoint cycles C a and C b joined by a path P c+3 (c -1) having only its end-vertices in common with the two cycles. By using a new cospectral invariant for (r, r + 1)-almost regular graphs, we will show that almost all dumbbell graphs (without cycle C 4 as a subgraph) are determined by the adjacency spectrum.

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