We generalize the Harary-Sachs theorem to k-uniform hypergraphs: codegree-d coefficient of characteristic polynomial a uniform hypergraph H can be expressed as weighted sum subgraph counts over certain multi-hypergraphs with d edges. include detailed description aforementioned and formula for their corresponding weights.

The nature of superluminal photon propagation in the gravitational field describing radiation from a time-dependent, isolated source (the Bondi-Sachs metric) is considered in an effective theory which includes interactions which violate the strong equivalence principle. Such interactions are, for example, generated by vacuum polarisation in conventional QED in curved spacetime. The relation of ...

The Goldberg-Sachs theorem has been very useful in constructing algebraically special exact solutions of Einstein vacuum equation. Most of the physical meaningful vacuum exact solutions are algebraically special. We show that the Goldberg-Sachs theorem is not true in linearized gravity. This is a remarkable result, which gives light on the understanding of the physical meaning of the linearized...

The Harary-Sachs theorem for k-uniform hypergraphs equates the codegree-d coefficient of adjacency characteristic polynomial a uniform hypergraph with weighted sum subgraph counts over certain multi-hypergraphs d edges. We begin by showing that classical graphs is indeed special case this general theorem. To end we apply generalized to leading coefficients various hypergraphs. In particular, pr...