Quantum graphs—networks composed of vertices connected by edges on which quantum wave dynamics are defined—have emerged as a versatile model for exploring the interplay between geometry, topology, and ...

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The second path matrix S(G) collects all the second paths in the graph G. Its characteristic polynomial shows some regularity in several particular graphs, such as paths, cycles, stars and complete ...

Mathematicians have proved that copies of smaller graphs can always be used to perfectly cover larger ones. On January 8, three mathematicians posted a proof of a nearly 60-year-old problem in ...