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Bounds on isoperimetric values of trees

โœ Scribed by B.V. Subramanya Bharadwaj; L. Sunil Chandran

Book ID
118435543
Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
467 KB
Volume
309
Category
Article
ISSN
0012-365X

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Let ฮป 1 (T ) and ฮป 2 (T ) be the largest and the second largest eigenvalues of a tree T , respectively. We obtain the following sharp lower bound for ฮป 1 (T ): where d i is the degree of the vertex v i and m i is the average degree of the adjacent vertices of v i . Equality holds if and only if T i