A Sufficiency Condition for Graphs to Admit Greedy Algorithm in Solving the Minimum Sum Vertex Cover Problem

Minimum sum vertex cover (MSVC) problem is a NP-Complete problem which arises in the context of designing efficient algorithms for solving semi-definite programs, and in the context of speeding up matrix computations. In this paper, in order to solve the MSVC problem, we address a new general problem: Precisely which graphs admit greedy algorithm in solving minimizing minimum sum vertex cover (MSVC) problem? We obtain a sufficiency condition for solving this problem; the graphs satisfying this condition have been called recurrent dominancy regular partition graphs (R-DRPG).