>

In this lecture, I will introduce some results on complexity of edge-related domination problems,  and  on characterizations for trees with properties about edge-related domination  parameters.

The concept of resistance distance originates from electrical network theory. The resistance distance distance between any two vertices of a connected graph G is defined as the sum of effective resistance between them in the electrical network constructed from G by replacing each edge of G with a (unit) resistor. In this talk, first of all, various methods for computing resistance distance are introduced. Then sum rules for resistance distances are established. Finally, an elegant recursion relation for computing resistance distance is derived.

In this talk, we introduce quasi-Laplacian matrix of fuzzy hypergraphs and study its spectral properties to explore the structural information of fuzzy hypergraphs. Positive semi-definiteness,  Rayleigh-Ritz theorem and Perron-Frobenius theorem for quasi-Laplacian matrix are concluded. We derive an upper and lower bound for the spectral radius of quasi-Laplacian matrix for k-uniform fuzzy hypergraphs. Two operations on fuzzy hypergraphs are defined. The change of the spectral radius of quasi-Laplacian matrix under these two operations is also investigated.

 责任编辑： 邹家浩