On the Annihilation Number of a Graph
نویسنده
چکیده
In this note, we introduce a graph invariant called the annihilation number and show that it is a sharp upper bound on the independence number. While the invariant does not distinguish between different graphs with the same degree sequence – since it is determined solely by the degrees – it still outperforms many well known upper bounds on independence number. The process which leads to the annihilation number is related to the process developed independently by Havel [17] and Hakimi [16] to determine whether or not there existed a simple graph with a given sequence of non-negative integers as its degree sequence. Key–Words: independence number, annihilation number, graph theory, residue
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