For a graph G, let 9(G) be the family of strong orientations of G, d(G) = min{d(D) / D t 9’ (G)} and p(G) = d(G) -d(G), where d(G) and d(D) are the diameters of G and D respectively. In this paper we show that p(G) = 0 if G is a Cartesian product of (I ) paths, and (2) paths and cycles, which satisfy some mild conditions.

It is known that every multigraph with an even number of edges has an even orientation (i.e., all indegrees are even). We study parity constrained graph orientations under additional constraints. We consider two types of constraints for a multigraph G = (V,E): (1) an exact conflict constraint is an edge set C ⊆ E and a vertex v ∈ V such that C should not equal the set of incoming edges at v; (2...

For a connected graph G containing no bridges, let D(G) be the family of strong orientations of G; and for any D ∈ D(G), we denote by d(D) the diameter of D. The orientation number −→ d (G) of G is defined by −→ d (G) = min{d(D)|D ∈ D(G)}. Let G(p, q;m) denote the family of simple graphs obtained from the disjoint union of two complete graphs K p and Kq by adding m edges linking them in an arbi...

For a connected graph G containing no bridges, let D(G) be the family of strong orientations of G; and for any D ∈ D(G), we denote by d(D) the diameter of D. The orientation number d (G) of G is defined by → d (G)=min{d(D) |D ∈ D(G)}. In this paper, we study the orientation numbers of a family of graphs, denoted by G(p, q;m), that are obtained from the disjoint union of two complete graphs Kp a...

In this paper we give a characterization of kernel-perfect (and of critical kernel-imperfect) arc-local tournament digraphs. As a consequence, we prove that arc-local tournament digraphs satisfy a strenghtened form of the following interesting conjecture which constitutes a bridge between kernels and perfectness in digraphs, stated by C. Berge and P. Duchet in 1982: a graph G is perfect if and ...

established definitions and theory), focuses on focuses on participants’ perspectives, and describes the results using expressive and persuasive language (Creswell, 1998). Qualitative research has some distinct characteristics (Flick et al, 2004), including: there is no single all-encompassing method, but a spectrum of methods from which one can be chosen depending on the research question it h...

Polycrystalline SnSe was synthesized by a melting-annealing-sintering process. X-ray diffraction reveals the sample possesses pure phase and strong orientation along [h00] direction. The degree of the orientations was estimated and the anisotropic thermoelectric properties are characterized. The polycrystalline sample shows a low electrical conductivity and a positive and large Seebeck coeffici...