Dress, AndreasUniBi; Stevanović, Dragance
Abstract / Bemerkung
Let G be a simple graph on n vertices with adjacency matrix A and distinct eigenvalues mu(1) > mu(2) > ... > mu(m). In his paper , Hoffman observed that G is a connected regular graph if and only if [GRAPHICS] holds where J is the n x n all-one matrix and I is the unit matrix. We study expressions of the form Pi(i=1)(t) (A - beta(t)I) in a more general context allowing us not only to derive Hoffman's identity in a new way, but also to compute, say, the rank of Pi(i=2)(m) (A-mu(i)I) and of Pi(mui not equal - mu1) (A-mu(i)I) for arbitrary simple graphs and to derive corresponding identities for the recently introduced classes of harmonic and semiharmonic graphs. (C) 2003. Elsevier Science Ltd. All rights reserved.
Hoffman's identity; harmonic graphs; semiharmonic graphs; regular graphs
Applied Mathematics Letters
Dress A, Stevanović D. Hoffman-type identities. Applied Mathematics Letters. 2003;16(3):297-302.
Dress, A., & Stevanović, D. (2003). Hoffman-type identities. Applied Mathematics Letters, 16(3), 297-302. https://doi.org/10.1016/S0893-9659(03)80047-2
Dress, A., and Stevanović, D. (2003). Hoffman-type identities. Applied Mathematics Letters 16, 297-302.
Dress, A., & Stevanović, D., 2003. Hoffman-type identities. Applied Mathematics Letters, 16(3), p 297-302.
A. Dress and D. Stevanović, “Hoffman-type identities”, Applied Mathematics Letters, vol. 16, 2003, pp. 297-302.
Dress, A., Stevanović, D.: Hoffman-type identities. Applied Mathematics Letters. 16, 297-302 (2003).
Dress, Andreas, and Stevanović, Dragance. “Hoffman-type identities”. Applied Mathematics Letters 16.3 (2003): 297-302.