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 ( , )...

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...

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...

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...

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...