Bounds for the Completely Positive Rank of a Symmetric Matrix over a Tropical Semiring

摘要

In this paper, we find an upper bound for the CP-rank of a matrix over atropical semiring, according to the vertex clique cover of the graph prescribedby the pattern of the matrix. We study the graphs that beget the patterns ofmatrices with the lowest possible CP-ranks and prove that any such graph musthave its diameter equal to 2.