OPTIMIZATION PROBLEMS ON THRESHOLD GRAPHS

During the last three decades, di®erent types of decompo-sitions have been processed in the ¯eld of graph theory. Among these wemention: decompositions based on the additivity of some characteristics of thegraph, decompositions where the adjacency law between the subsets of the par-tition is known, decompositions where the subgraph induced by every subsetof the partition must have predeterminate properties, as well as combinationsof such decompositions.In this paper we characterize threshold graphs using the weakly decom-position, determine: density and stability number, Wiener index and Wienerpolynomial for threshold graphs