This study presents models and heuristics for solving the strong network orientation problem (SNOP), which can model several tactical optimization problems of setting directions in urban networks. The objective is to set an each edge undirected graph such that resulting digraph strongly connected total travel distance between any pair nodes minimized (or maximized). Investigating as SNOP motiva...

A graph G = (V, E) is representable if there exists a word W over the alphabet V such that letters x and y alternate in W if and only if (x, y) ∈ E for each x 6= y. If W is k-uniform (each letter of W occurs exactly k times in it) then G is called k-representable. The minimum k for which a representable graph G is k-representable is called its representation number. In this paper we give a char...

The concept of forced orientation of graphs was introduced by G. Chartrand et al. in 1994. If, for a given assignment of directions to a subset S of the edges of a graph G, there exists an orientation of E(G) \ S, so that the resulting graph is strongly connected, then that given assignment is said to be extendible to a strong orientation of G. The forced strong orientation number fD(G), with r...

We employ monochromatized electron energy loss spectroscopy to study Ti3SiC2 and Ti3AlC2. By probing individual grains aligned along different axes in bulk polycrystalline Ti3SiC2 and Ti3AlC2, this approach enables determination of the anisotropy of the dielectric functions and an estimate of the free-electron lifetime in different orientations. The dielectric functions are characterized by str...

We consider the problem of reorienting an oriented matroid so that all its cocircuits are 'as balanced as possible in ratio'. It is well known that any oriented matroid having no coloops has a totally cyclic reorientation, a reorientation in which every signed cocircuit B = {B + , B − } satisfies B + , B − = ∅. We show that, for some reorientation, every signed cocircuit satisfies 1/f (r) ≤ |B ...

An orientation of a graph is acyclic (totally cyclic) if and only if it is a “positive orientation” of a nowhere-zero integral tension (!ow). We unify the notions of tension and !ow and introduce the so-called tension-!ows so that every orientation of a graph is a positive orientation of a nowhere-zero integral tension-!ow. Furthermore, we introduce an (integral) tension-!ow polynomial, which g...

A sufficient condition for graphs with circular flow index less than 4 is found in this paper. In particular, we give a simple proof of a result obtained by Galluccio and Goddyn (Combinatorica, 2002), and obtain a larger family of such graphs. We refer readers to [1], [2] and [7] for the standard terminology and notations in this paper. The following theorem was proved by Galluccio and Goddyn. ...

Gioan showed that the number of cycle reversing classes of totally cyclic orientations of a given graph can be calculated as an evaluation of the corresponding Tutte polynomial. We note that the concept of cycle reversing classes of orientations coincides with that of Eulerianequivalence classes considered by Chen and Stanley, and Kochol. Based on this coincidence, we give a bijective proof of ...