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Note on the energy of regular graphs

✍ Scribed by Xueliang Li; Yiyang Li; Yongtang Shi


Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
97 KB
Volume
432
Category
Article
ISSN
0024-3795

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Let G be a 2-connected d-regular graph on n rd (r 3) vertices and c(G) denote the circumference of G. Bondy conjectured that c(G) 2nΓ‚(r&1) if n is large enough. In this paper, we show that c(G) 2nΓ‚(r&1)+2(r&3)Γ‚(r&1) for any integer r 3. In particular, G is hamiltonian if r=3. This generalizes a resu