A k-independent set in a connected graph is a set of vertices such that any two vertices in
the set are at distance greater than k in the graph. The k-independence number of a graph …

This paper generalizes and unifies the existing spectral bounds on the k-independence
number of a graph, which is the maximum size of a set of vertices at pairwise distance …

The k th power of a graph G=(V, E), G k, is the graph whose vertex set is V and in which two
distinct vertices are adjacent if and only if their distance in G is at most k. This article proves …

In this paper, we obtain two spectral upper bounds for the k-independence number of a
graph which is the maximum size of a set of vertices at pairwise distance greater than k. We …

The k-independence number of a graph is the maximum size of a set of vertices at pairwise
distance greater than k. A graph is called k-partially walk-regular if the number of closed …

The k-independence number of a graph G is the maximum size of a set of vertices at
pairwise distance greater than k. In this paper, for each positive integer k, we prove sharp …

Let G be a graph of order n (G) n (G) and vertex set V (G). Given a set S ⊆ V (G) S⊆ V (G),
we define the external neighbourhood of S as the set N_e (S) N e (S) of all vertices in V (G) …

For k≥ 1, the k-independence number α k of a graph is the maximum number of vertices that
are mutually at distance greater than k. The well-known inertia and ratio bounds for the (1-) …

Abstract A set S⊆ V (G) is a k-independent set of a graph G if the distance between every
two vertices of S is greater than k. The k-independence number α k (G) of G is the maximum …

We present a simple, yet efficient, heuristic for finding a large 2-independent set of regular
graphs. We analyse the average-case performance of this heuristic, which is a randomised …