Answering some questions of Gutman, we show that, except for four specific trees, every connected graph G of order n, with no cycle of order 4 and with maximum degree at most 3, satisfies |μ1|+ · · ·+ |μn| ≥ n, where μ1, . . . , μn are the eigenvalues of G. We give some general results and state two conjectures. AMS classification: 05C50

Let G be a connected graph. The vertex-set and edge-set of G denoted by V(G) and E(G) respectively. The distance between the vertices u and v, d(u,v), in a graph is the number of edges in a shortest path connecting them. Two graph vertices are adjacent if they are joined by a graph edge. The degree of a vertex ( ) i V G ∈ is the number of vertices joining to i and denoted by ( ) v i . The ( , )...

RESUME In this paper, two different methods for fractional vegetation cover (FVC) retrieval from CHRIS (Compact High Resolution Imaging Spectrometer) data based on vegetation indices have been analyzed. The first method uses NDVI (Normalized Difference Vegetation Index) values, as suggested, among others, by Carlson and Ripley (1997) and Gutman and Ignatov (1998), and the second method uses VAR...

Multi-protocol attacks due to protocol interaction has been a notorious problem for security. Gutman-Thayer proved that they can be prevented by ensuring that encrypted messages are distinguishable across protocols, under a free algebra [1]. In this paper, we prove that a similar suggestion prevents these attacks under commonly used operators such as Exclusive-OR, that induce equational theorie...

We present a simple randomized polynomial time algorithm to approximate the mixed discriminant of n positive semidefinite n×n matrices within a factor 2. Consequently, the algorithm allows us to approximate in randomized polynomial time the permanent of a given n×n non-negative matrix within a factor 2. When applied to approximating the permanent, the algorithm turns out to be a simple modifica...

We show that the absolute value of the determinant of a matrix with random independent (but not necessarily i.i.d.) entries is strongly concentrated around its mean. As an application, we show that Godsil–Gutman and Barvinok estimators for the permanent of a strictly positive matrix give subexponential approximation ratios with high probability. A positive answer to the main conjecture of the p...

A graph, consisting of undirected edges, can be represented as a sum of two digraphs, consisting of oppositely oriented directed edges. Gutman and Plath in [J. Serb. Chem. Soc. 66 (2001), 237–241] showed that for annulenes, the eigenvalue spectrum of the graph is equal to the sum of the eigenvalue spectra of respective two digraphs. Here we exhibit a number of other graphs with this property.

Florence F. Roussotte,1,3 Boris A. Gutman,3,4 Sarah K. Madsen,3,4 John B. Colby,1 and Paul M. Thompson1,2,3,4,5 for the Alzheimer’s Disease Neuroimaging Initiative* 1Department of Neurology, and 2Department of Psychiatry, Semel Institute, David Geffen School of Medicine, University of California, Los Angeles, Los Angeles, California 90095, 3Imaging Genetics Center, and 4Departments of Neurology...

Topological polynomial and indices based on the distance between vertices of a connected graph are widely used in chemistry to establish relation structure properties molecules. In similar way, chromatic versions certain topological related have also been discussed recent literature. this paper, we present Schultz Gutman polynomials expanded form Hosoya polynomials, then derive these for specia...