In this paper, we determine the largest number of maximal independent sets among all connected graphs of order n, which contain at most one cycle. We also characterize those extremal graphs achieving this maximum value. As a consequence, the corresponding results for graphs with at most one cycle but not necessarily connected are also given.

In this paper, we show that every chordal graph with n vertices and m edges admits an additive 4-spanner with at most 2n− 2 edges and an additive 3-spanner with at most O(n log n) edges. This significantly improves results of Peleg and Schäffer from [Graph Spanners, J. Graph Theory 13 (1989) 99–116]. Our spanners are additive and easier to construct.An additive 4-spanner can be constructed in l...

A previous application of extreme-value statistics to the ®rst, second and third largest geomagnetic storms per solar cycle for nine solar cycles is extended to fourteen solar cycles (1844±1993). The intensity of a geomagnetic storm is measured by the magnitude of the daily aa index, rather than the half-daily aa index used previously. Values of the conventional aa index (1868± 1993), supplemen...

In eukaryotes, initiation of DNA replication requires the activity of the origin recognition complex (ORC). The largest subunit of this complex, Orc1p, has a critical role in this activity. Here we have studied the subnuclear distribution of the overexpressed human Orc1p during the cell cycle. Orc1p is progressively degraded during S-phase according to a spatio-temporal program and it never col...

A multi-instrumental analysis of the meridional ionospheric response is presented over Europe during two largest ICME-driven geomagnetic storms solar cycle #24 maximum. Data from 5 European digisonde stations, ground-based Global Navigation Satellite System, Total Electron Content (GNSS TEC), ratio TEC difference (rTEC), as well Swarm and Thermosphere, Ionosphere, Mesosphere, Energetics Dynamic...

Based on a plug-in hybrid car equipped with 1.5L turbocharged direct injection gasoline engine, this paper studies the emission and fuel consumption characteristics of prototype vehicle under three different cycle conditions, WLTC city, CLTC-P. The results show that for four pollutants: CO, THC, NMHC NOx, city emissions are largest, smallest, CLTC-P middle. For N2O, has largest combined emissio...

We present evidence for chaos and generalised multistability in a mesoscopic model of the electroencephalogram (EEG). Two limit cycle attractors and one chaotic attractor were found to coexist in a two-dimensional plane of the tendimensional volume of initial conditions. The chaotic attractor was found to have a moderate value of the largest Lyapunov exponent (3.4 s−1 base e) with ∗Correspondin...

The hyper-Kirchhoff index is introduced when the hyper-Wiener operator is applied to the resistance-distance matrix of a connected graph. We give lower and upper bounds for the hyper-Kirchhoff index, and determine the n-vertex unicyclic graphs with the smallest, the second and the third smallest as well as the largest, the second and the third largest hyper-Kirchhoff indices for n ≥ 5. We also ...

Abstract. Given a finite abelian group G, consider the complete graph on the set of all elements of G. Find a Hamiltonian cycle in this graph and for each pair of consecutive vertices along the cycle compute their sum. What are the smallest and the largest possible number of sums that can emerge in this way? What is the expected number of sums if the cycle is chosen randomly? How the answers ch...

We consider the following problem: Given a rectangle containing N points, find the largest area subrectangle with sides parallel to those of the original rectangle which contains none of the given points. If the rectangle is a piece of fabric or sheet metal and the points are flaws, this problem is finding the largest-area rectangular piece which can be salvaged. A previously known result [13] ...