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Some topological indices of certain classes of cycloalkenes
Veena Mathad,Padmapriya P,Ismail Naci CANGUL 장전수학회 2019 Proceedings of the Jangjeon mathematical society Vol.22 No.2
Let G = (V;E) be a simple connected molecular graph. The degree di of any vertex vi in G is the number of edges incident with vi and the eccentricity ei of vi is the largest distance between vi and any other vertex of G. In this paper, we establish general formulae for some degree based and eccentricity based topological indices of cycloalkenes.
K^th-eccentricity index of graphs
Veena Mathad,PARVATHI,Ismail Naci CANGUL 장전수학회 2022 Proceedings of the Jangjeon mathematical society Vol.25 No.2
The molecular topological descriptors are the numerical in- variants of a molecular graph and are very useful for predicting their physical properties, chemical reactivity and bioactivity. A variety of such indices are studied and used in theoretical chemistry and phar- maceutical research related to drugs and also in different fields. The main classes of topological graph indices are those based on vertex de- grees, distances, and graph parameters like eccentricity. In this pa- per, we introduce kth-eccentricity index of graphs. Also we compute kth-eccentricity index of some standard graphs including some wind- mill graphs and molecular graphs of cycloalkenes. Further, we obtain lower and upper bounds for the kth-eccentricity index in terms of other topological indices.
Bounds for the First Zagreb Eccentricity Index and First Zagreb Degree Eccentricity Index
Padmapriya, P.,Veena, Mathad Department of Mathematics 2018 Kyungpook mathematical journal Vol.58 No.2
The first Zagreb eccentricity index $E_1(G)$ of a graph G is defined as the sum of squares of the eccentricities of the vertices. In this paper some bounds for the first Zagreb eccentricity index and first Zagreb degree eccentricity index are computed.
Ali Sahal,Veena Mathad 장전수학회 2012 Proceedings of the Jangjeon mathematical society Vol.15 No.4
Let G = (V1, V2,E) be a bipartite graph. Then G is called cocomplete bipartite graph, if for any two vertices u, v 2 Vi, i=1,2 there exists P3 containing them. In this paper, we study some properties of cocomplete bipartite graphs. We obtain the necessary and sufficient condition for a cocomplete bipartite graph to be complete bipartite. We also study the condition under which a bipartite graph becomes cocomplete bipartite graph. Further, we establish the relation between balanced bipartite graph and cocomplete bipartite graph. We find the bound for the number of edges of cocomplete bipartite graph.
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.
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.
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