China 
Africa 
Explore chapters and articles related to this topic
Wiener Index of Tensor Product of Cycle Graph and Some Other Graphs
Published in N. P. Shrimali, Nita H. Shah, Recent Advancements in Graph Theory, 2020
Let G = (V(G), E(G)) and H = (V(H), E(H)) be finite, simple and connected graphs. Then tensor product G ⊗ H of G and H is defined as the graph with vertex set V(G ⊗ H) = V(G) × V(H) and edge set {(x,y)(x′,y′):xx′∈E(G)&yy′∈E(H),x,x′∈V(G),y,y′∈V(H)}. The tensor product graph is a very well known graph product and has been studied in detail ([2],[3]).
The Directional Discrete Cosine Transform
Published in Humberto Ochoa-Domínguez, K. R. Rao, Discrete Cosine Transform, 2019
Humberto Ochoa-Domínguez, K. R. Rao
Then, we determine where the edges must be placed in the product graphProduct graph. We see that e is an edge of the product graph if and only if e = (ui, vk)(um, vn), where either i = m and vk,vn∈E2 or k = n and ui,um∈E1.
Designing the Product
Published in David M. Anderson, Design for Manufacturability, 2020
The graph “Product Cost vs. Time” (Figure 1.1) shows that 60% of the products lifetime cumulative cost is committed by the concept/architecture phase. Similarly this phase has the most significant effect on quality, reliability, serviceability, flexibility, customizability, etc. The graphs, Traditional vs Advanced Team Participation Models (Figure 2.1), show that thoroughly optimizing the architecture phase results in faster ramps and eliminates post-release problem solving for volume, quality, and productivity. Similarly, Figure 3.1 shows that the real time-to-market can be cut almost in half by thorough up-front work by spending a third of the time line on optimizing architecture, instead of rushing through that phase.
Tensor and Cartesian products for nanotori, nanotubes and zig–zag polyhex nanotubes and their applications to 13C NMR spectroscopy
Published in Molecular Physics, 2021
Medha Itagi Huilgol, V. Sriram, Krishnan Balasubramanian
Graph products facilitate computations of the properties of larger graphs in terms of the constituting graphs. For this reason graph products have been applied to computing the topological indices such as the PI index, Wiener index, Szeged index of carbon nanotubes and nanotori [1–3,27,58,59] by the use of graph products. The 4-nanotubes can be generated as the cartesian product for some integral values of m and n, where is a cyclic graph containing m vertices while is a path containing n vertices. In general by varying m and n we can obtain graph-theoretical representations of various nanotubular structures. Likewise the cartesian product generates nanotori, which are donut shaped structures of various lengths and diameter.