Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9498198 | Linear Algebra and its Applications | 2005 | 7 Pages |
Abstract
An eigenvalue of a graph G is called main eigenvalue if it has an eigenvector the sum of whose entries is not equal to zero. Hoffman [A.J. Hoffman, On the polynomial of a graph, Amer. Math. Monthly 70 (1963) 30-36] proved that G is a connected k-regular graph if and only if nâi=2t(A-λiI)=âi=2t(k-λi)·J, where I is the unit matrix and J the all-one matrix and λ1 = k, λ2, â¦, λt are all distinct eigenvalues of adjacency matrix A(G). In this note, some generalizations of Hoffman identity are presented by means of main eigenvalues.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Yaoping Hou, Feng Tian,