"This allows us to exploit the exact, efficient solutions for planar spin glasses. For non-planar graphs, such solutions are computationally intractable," explained the researchers.

Graphs and networks are powerful tools for representing connections or relationships between objects or people. They belong to a branch of mathematics called graph theory which is quite distinct from ...

The evolution of web search engines offers an instructive example, showing how knowledge can be extracted from unstructured sources and refined over time into a structured, interconnected graph.

How to Graph a Demand Schedule It can be useful to graph a demand and supply schedules for a visual representation of the market for a particular product.

Gladkov, Pak, and Zimin found many small-graph examples that satisfied the conjecture, but in the end, those did not reflect the more complicated, less intuitive graphs they could build when given ...

A new method is proposed to synthesize arbitrary-tiled arrays fitting multiple, generally conflicting, requirements for multiantenna systems operating beyond 100 GHz. The array structure is decomposed ...

Arbitrary Subarrayed Planar Array Antenna With Sidelobe Level Control Based on a Graph Theory Abstract:A new method is proposed to synthesize arbitrary-tiled arrays fitting multiple, generally ...

ABSTRACT: The Total Coloring Conjecture (TCC) proposes that every simple graph G is (Δ + 2)-totally-colorable, where Δ is the maximum degree of G. For planar graph, TCC is open only in case Δ = 6. In ...

ABSTRACT: The Total Coloring Conjecture (TCC) proposes that every simple graph G is (Δ + 2)-totally-colorable, where Δ is the maximum degree of G. For planar graph, TCC is open only in case Δ = 6. In ...