An algorithm for finding the Independence Number of a graph

TL;DR

This paper introduces algorithms to find a split graph with the same independence number as a given graph and to compute the independence number directly from the adjacency matrix.

Contribution

It presents the first algorithms for constructing a split graph with the same independence number and for calculating the independence number from the adjacency matrix.

Findings

Existence of a split graph with the same independence number for any connected graph

Algorithms for constructing such split graphs from degree sequences

Algorithms for computing independence number from adjacency matrices

Abstract

In this paper, we prove that for every connected graph G, there exists a split graph H with the same independence number and the same order. Then we propose a first algorithm for finding this graph, given the degree sequence of the input graph G. Further, we propose a second algorithm for finding the independence number of G, given the adjacency matrix of G.