The purpose of this paper is to obtain a necessary and sufficient condition for the tensor product of two or more graphs to be connected, bipartite or eulerian. Also, we present a characterization of the duplicate graph $G 1 K_2$ to be unicyclic. Finally, the girth and the formula for computing the number of triangles in the tensor product of graphs are worked out.

The rendering process reduces the 3D geometry to a set of 2D triangles in the image plane. The projection from 3D is standard. The projected triangles are clipped and sorted so that the final collection of triangles in a pixel do not overlap each other. So at frame f , the image plane holds a collection of pixels Pk, k = 1, . . .M , each of which contains a set of 2D nonoverlapping triangles {T...

A triple of vertices in a graph is a frustrated triangle if it induces an odd number of edges. We study the set Fn ⊂ [0, n 3  ] of possible number of frustrated triangles f (G) in a graph G on n vertices. We prove that about two thirds of the numbers in [0, n3/2] cannot appear in Fn, and we characterise the graphs G with f (G) ∈ [0, n3/2]. More precisely, our main result is that, for each n ≥...

High-energy-density (HED) hydrodynamics studies such as those relevant to inertial confinement fusion and astrophysics require highly disparate densities, temperatures, viscosities, other diffusion parameters over relatively short spatial scales. This presents a challenge for high-order accurate methods effectively resolve the at these scales, particularly in presence of diffusion. A significan...