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Sharp lower bounds of the least eigenvalue of planar graphs

โœ Scribed by Yuan Hong; Jin-Long Shu

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
75 KB
Volume
296
Category
Article
ISSN
0024-3795

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โœฆ Synopsis

Let G be a simple graph with n P 3 vertices and orientable genus g and non-orientable genus h. We deยฎne the Euler characteristic vq of a graph G by vq maxf2 ร€ 2gY 2 ร€ 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 ร€ 2n ร€ vq p X

In particular, if G is the planar graph, then kq P ร€ 2n ร€ 4 p the equality holds if and only if q u 2Ynร€2 . Further, we have same result of seriesยฑ parallel graph.

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