A note on Hoffman-type identities of graphs
نویسندگان
چکیده
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 n ∏t i=2(A− λiI ) = ∏t i=2(k − λi) · J , where I is the unit matrix and J the all-one matrix and λ1 = k, λ2, . . . , 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. © 2005 Elsevier Inc. All rights reserved. AMS classification: 05C50; 05C75
منابع مشابه
A note on‘‘A case study approach for developing a project performance evaluation system”
The major aim of this research is benchmarking Honeywell Federal Manufacturing &Technologies projects using Data Envelopment Analysis (DEA) technique and to compare the results with that of published recently in Qing Cao, James J. Hoffman Qing Cao, James J. Hoffman. (2011). A case study approach for developing a project performance evaluation system. International Journal of Project Managem...
متن کاملThermal Convection in a (Kuvshiniski-type) Viscoelastic Rotating Fluid in the Presence of Magnetic Field through Porous Medium (TECHNICAL NOTE)
The effect of magnetic field on an incompressible (Kuvshiniski-Type) viscoelastic rotating fluid heated from below in porous medium is considered. For the case of stationary convection, magnetic field and medium permeability have both stabilizing and destabilizing effect on the thermal convection under some conditions whereas rotation has a stabilizing effect on the thermal convection. In the...
متن کاملA note on vague graphs
In this paper, we introduce the notions of product vague graph, balanced product vague graph, irregularity and total irregularity of any irregular vague graphs and some results are presented. Also, density and balanced irregular vague graphs are discussed and some of their properties are established. Finally we give an application of vague digraphs.
متن کاملA NOTE ON THE COMMUTING GRAPHS OF A CONJUGACY CLASS IN SYMMETRIC GROUPS
The commuting graph of a group is a graph with vertexes set of a subset of a group and two element are adjacent if they commute. The aim of this paper is to obtain the automorphism group of the commuting graph of a conjugacy class in the symmetric groups. The clique number, coloring number, independent number, and diameter of these graphs are also computed.
متن کامل