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Distance majorization integrity of graphs
SULTAN SENAN MAHDE,Veena Mathad 장전수학회 2017 Proceedings of the Jangjeon mathematical society Vol.20 No.3
The concept of distance majorization integrity is introduced as a new measure of the stability of a graph G and it is dened as DMI(G) = min{|S| + m(G - S)}, where S is a distance majorization set and m(G - S) is the order of a maximum component of G - S. The distance majorization integrity of some graphs is obtained. The relations between distance majorization integrity and other parameters are determined. Also a distance majorization integrity of corona of some graphs are computed
ACCESSIBILITY INTEGRITY OF GRAPHS
SULTAN SENAN MAHDE,Veena Mathad,Ismail Naci CANGUL 장전수학회 2021 Advanced Studies in Contemporary Mathematics Vol.31 No.1
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 dened 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.
SHADI IBRAHIM KHALAF,Veena Mathad,SULTAN SENAN MAHDE,Ismail Naci CANGUL 장전수학회 2022 Proceedings of the Jangjeon mathematical society Vol.25 No.2
For a graph G having at least one edge, the minimum number of edges which we can remove from G such that the re- sulting graph has hub number larger than the hub number of G is called the pivot number p(G) of G. The values of pivot number for several classes of graphs are computed, and we determine the pivot number of join and corona products. Also some bounds for this parameter are obtained.