On the Restrained Cost Eective Sets of Some Special Classes of Graphs
Darwin P. Mangubat
Mathematics Department, College of Arts and Sciences, Central Mindanao University, Musuan, Maramag, Bukidnon.
Isagani S. Cabahug, Jr. *
Mathematics Department, College of Arts and Sciences, Central Mindanao University, Musuan, Maramag, Bukidnon.
*Author to whom correspondence should be addressed.
Abstract
Let G be a nontrivial, undirected, simple graph. Let S be a subset of V (G). S is a restrained cost effective set of G if for each vertex v in S, degS(v) \(\leq\) degV (G)rS(v) and the subgraph induced by the vertex set, V (G) r S has no isolated vertex. The maximum cardinality of a restrained cost effective set is the restrained cost effective number, CEr(G). In this paper, the restrained cost effective sets of paths, cycles, complete graphs, complete product of graphs and graphs resulting from line graph of graphs with maximum degree of 2 were characterized. As a direct consequence, the bounds or exact values for the restrained cost effective number were determined as well.
Keywords: Restrained cost effective set, restrained cost effective number, line graph