ACCESSIBILITY INTEGRITY OF GRAPHS
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In this paper, the concept of accessibility integrity is intro- duced as a new measure of the stability of a graph G and it is de ned as AI(G) = minfjSj + m(G - S)g; where S is an accessible set and m(G - S) is the order of a maximum component of G - S. First, the accessibility integrity of some graphs is obtained and the relations between accessibility integrity and other parameters are determined. Next AI-changing and AI-stable graphs are studied. The properties of AI-stellar and just AI-stellar graph are discussed. It is shown that the accessibility integrity is much stronger characteristic compared to the integrity in determining the stability of a graph. The effect of vertex deletion on the accessibility integrity of a graph is studied. Also a recent problem called the inverse problem is completely solved for the accessibility integrity of a graph by showing that there exists at least one graph with accessibility integrity equal to r for all integers r ≥ 4.
Abstract
In this paper, the concept of accessibility integrity is intro- duced as a new measure of the stability of a graph G and it is de ned as AI(G) = minfjSj + m(G - S)g; where S is an accessible set and m(G - S) is the order of a maximum component of G - S. First, the accessibility integrity of some graphs is obtained and the relations between accessibility integrity and other parameters are determined. Next AI-changing and AI-stable graphs are studied. The properties of AI-stellar and just AI-stellar graph are discussed. It is shown that the accessibility integrity is much stronger characteristic compared to the integrity in determining the stability of a graph. The effect of vertex deletion on the accessibility integrity of a graph is studied. Also a recent problem called the inverse problem is completely solved for the accessibility integrity of a graph by showing that there exists at least one graph with accessibility integrity equal to r for all integers r ≥ 4.
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