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Further results on the least eigenvalue of connected graphs

✍ Scribed by Miroslav Petrović; Tatjana Aleksić; Slobodan Simić

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
289 KB
Volume
435
Category
Article
ISSN
0024-3795

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📜 SIMILAR VOLUMES

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Let G be a simple graph with n P 3 vertices and orientable genus g and non-orientable genus h. We de®ne the Euler characteristic vq of a graph G by vq maxf2 À 2gY 2 À hg. Let kq be the least eigenvalue of the adjacency matrix A of G. In this paper, we obtain the following lower bounds of kq kq P À 2

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Among the cacti with n vertices and k cycles we determine a unique cactus whose least eigenvalue is minimal. We also explore cacti with n vertices and among them, we find a unique cactus whose least eigenvalue is minimal.