On the Restrained Cost Eective Sets of Some Special Classes of Graphs

LetGbe a nontrivial, undirected, simple graph. LetSbe a subset ofV(G).Sis a restrained costeffective set ofGif for each vertexvinS, degS(v)≤degV(G)rS(v) and the subgraph inducedby the vertex set,V(G)rShas no isolated vertex. The maximum cardinality of a restrainedcost effective set is the restrained cost effective number,CEr(G). In this paper, the restrainedcost effective sets of paths, cycles, complete graphs, complete product of graphs and graphsresulting from line graph of graphs with maximum degree of 2 were characterized. As a directconsequence, the bounds or exact values for the restrained cost effective number were determinedas well.