Graphs with given k-independence number

Abstract

The concept of k-independent number, introduced by Fink and Jacob- son, is a natural generalization of classical independence number. A k- independent set is a set of vertices whose induced subgraph has maximum degree at most k. The k-independence number of G, denoted by is defined as the maximum cardinality of a k-indepcndent set of G. For a graph of order n, we have 1 < αk(G) < n. In this paper, graphs with a∗(G) = 1,2,71 - 2,71- l,n are characterized, respectively. © 2018 Utilitas Mathematica Publishing Inc. All rights reserved.