Enumeration of structure-sensitive graphical subsets: Theory

Abstract

THE NECESSARY MATHEMATICAL MACHINERY IS DEVELOPED FOR ENUMERATION OF THE FOLLOWING TYPES OF SPECIAL SUBSETS OF THE VERTICES OR EDGES OF A GENERAL GRAPH: (i) independent sets, (ii) connected sets, (iii) point and line covers, (iv) externally stable sets, (v) kernels, and (vi) irredundant sets.