In this paper characterizations of connected unicyclic and bicyclic graphs in terms of the degree sequence, as well as the graphs in these classes minimal with respect to the degree distance are given. © 2007 Elsevier B.V. All rights reserved.

We address the problem of approximating the distance of sparse graphs from having some predefined property P. The distance of G from having P is εP(G) if the minimum number of edge modifications needed in order to enforce P on G is εP(G) · m̄, where m̄ is an upper bound on the number of edges in the graph. When dealing with bounded-degree graphs of maximal degree d we take m̄ = dn, where n is the ...

We present an algorithm for calculating the quartet distance between two evolutionary trees of bounded degree on a common set of n species. The previous best algorithm has running time O(d2n2) when considering trees, where no node is of more than degree d. The algorithm developed herein has running time O(d9n log n)) which makes it the first algorithm for computing the quartet distance between ...

In this contribution, we first investigate sharp bounds for the reciprocal sum-degree distance of graphs with a given matching number. The corresponding extremal graphs are characterized completely. Then we explore the k-decomposition for the reciprocal sum-degree distance. Finally,we establish formulas for the reciprocal sum-degree distance of join and the Cartesian product of graphs.

Experimental and theoretical study of wetting properties of patterned Si surfaces with cylindrical flat-top pillars of various sizes and pitch distances is presented. The values of the contact angle (CA), contact angle hysteresis (CAH) and tilt angle (TA) are measured and compared with the theoretical values. Transition from the composite solid-liquid-air to the homogeneous solid-liquid interfa...

Degree Three Chordal Rings and N2R Topologies are useful for physial and optical network topologies due to the combination of short distances, regularity and low degrees. In this paper we show how distances in terms of average distances and diameters can be significantly decreased by using chords of different lengths. These topologies are slightly less symmetric than the traditional ones, but t...

A new scheme, sketch-map, for obtaining a low-dimensional representation of the region of phase space explored during an enhanced dynamics simulation is proposed. We show evidence, from an examination of the distribution of pairwise distances between frames, that some features of the free-energy surface are inherently high-dimensional. This makes dimensionality reduction problematic because the...

MORE THAN twenty years ago, the author (Gutenberg, 1926) pointed out that the longitudinal waves of shallow earthquakes decrease considerably in amplitude at epicentral distances between a few (say 2) degrees and about 15 degrees. At greater distances the amplitudes become again rather large, at 16 ° epicentral distance about as large as at 2 °. With further increase in epicentral distance the ...

In this paper we study the problem of conditioning a belief function b with respect to an event A by geometrically projecting such belief function onto the simplex associated with A in the simplex of all belief functions. Two different such simplices can be defined, as each belief function can be represented as the vector of its basic probability values or the vector of its belief values. We sh...

The degree distance of a graph G is     , 1 1 1 2 n n i j i i j D G d d L        j , where and i d j d are the degrees of vertices , and is the distance between them. The Wiener index is defined as   , i j v v V G  , i j L   , 1 1 1 2 n n i j i j W G L      . An elegant result (Gutman; Klein, Mihalić,, Plavšić and Trinajstić) is known regarding their correlation, that   ...