Signed Graphs

Jue Wang

香港科技大学


Abstract

Signed graphs have been studied by many people since early of 1960s. The current most interesting results were made by Zaslavsky. Their work is based on Matroid Theory. I consider signed graphs by introducing algebraic and geometric ideas, which rise more new structures and beautiful results. First, I finished constructing circuit space, bond space in use of torsion 2, and proved their orthogonal relation. Second, my works were to prove the relation between chromatic space and tension space. In particular, I found the relation between Eulerian space and circuit space. Finally, I did some work on their lattices, coloring polynomials, integral tension polynomials and modular tension polynomials in use of reciprocity law of Ehrhart polynomials.