  We introduce the signless 1-Laplacians and the dual Cheeger constants on
simplicial complexes. The connection of its spectrum to the combinatorial
properties like independence number, chromatic number and dual Cheeger constant
is investigated. Our estimates can be comparable to Hoffman's bounds in virtue
of Laplacian on simplicial complexes. An interesting inequality relating
multiplicity of the largest eigenvalue, independence number and chromatic
number are provided, which could be regarded as a variant version of Lovasz
sandwich theorem. Also, the behavior of the operator under the topological
operations of wedge and duplication of motifs is studied. The Courant nodal
domain theorem in spectral theory is extended to the case of signless
1-Laplacian on complexes.
