Majority reinforcement number.

A two-valued function defined on the vertices of a graph , is a majority dominating function if the sum of its function values over at least half the closed neighborhoods is at least one. That is, for at least half the vertices , , where consists of and every vertex adjacent to . The majority domination number of a graph , denoted , is the minimum value of over all majority dominating functions of . The majority reinforcement number of , denoted by , is defined to be the minimum cardinality of a set of edges such that . In this paper, we initiate the study of majority reinforcement number and determine the exact values of for paths and cycles. [ABSTRACT FROM AUTHOR]