On the independence number of graphs related to a polarity

The independence number for polarity graphs of even order planes

In this paper, we use coherent configurations to obtain new upper bounds on the independence number of orthogonal polarity graphs of projective planes of even order. In the case of classical planes of square even order, these bounds differ only by 1 from the size of the largest known independent sets.

On the independence number of random graphs

On the k-independence number in graphs

For an integer k ≥ 1 and a graph G = (V,E), a subset S of V is kindependent if every vertex in S has at most k − 1 neighbors in S. The k-independent number βk(G) is the maximum cardinality of a kindependent set of G. In this work, we study relations between βk(G), βj(G) and the domination number γ(G) in a graph G where 1 ≤ j < k. Also we give some characterizations of extremal graphs.

A new lower bound on the independence number of graphs

We propose a new lower bound on the independence number of a graph. We show that our bound compares favorably to recent ones (e.g. [12]). We obtain our bound by using the Bhatia-Davis inequality applied with analytical results (minimum, maximum, expectation and variance) of an algorithm for the vertex cover problem.

On the independence number of the Erdös-Rényi and projective norm graphs and a related hypergraph

The Erdős-Rényi and Projective Norm graphs are algebraically defined graphs that have proved useful in supplying constructions in extremal graph theory and Ramsey theory. Their eigenvalues have been computed and this yields an upper bound on their independence number. Here we show that in many cases, this upper bound is sharp in order of magnitude. Our result for the Erdős-Rényi graph has the f...