Some Topics of Special Interest in Graph Theory

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Discussion On Some Important Topics in Graph Theory

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Study of Some Interesting Topics in the Theory of Graphs

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Some Investigations in the Theory of Graphs

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Discussion on some interesting topics in Graph Theory

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Design and Implementation of Small Multiples Matrix-based Visualisation to Monitor and Compare Email Socio-organisational Relationships

One of the fundamental organisational questions is how organisations identify anomalies, monitor and compare email communications between staff-staff or staff-clients or staff-customers relationships on a daily basis. The tenacious and substantial relationships are built by the combination of timely replies, frequent engagement and deep interaction between the individuals. To watchdog this periodically, we need an interactive visualisation tool that can help organisational analysts to reconnect some lost relationships and/or strengthen an existing relationship or in some cases identify inside persons (anomalies). From our point of view, Social Intelligence (SI) in an organisation is a combination of self-, social- and organisational-awareness that will help in managing complex socio-organisational changes and can be interpreted in terms of socio-organisational communication efficacy (that is, one's confidence in one's ability to deal with social and organisational information). We considered a case study, an Enron Organisation Email Scandal, to understand the relationships of staff during various parts of the years and we conducted a workshop study with legal experts to gain insights on how they carry out investigation/analysis with respect to email relationships. The outcomes of the workshop helped us develop a novel small multiples matrix-based visualisation in collaboration with our industrial partner, Red Sift UK, to find anomalies, monitor and compare how email relationships change over time and how it defines the meaning of socio-organisational communication efficacy

3-Total Super Sum Cordial Labeling by Applying Operations on some Graphs

The sum cordial labeling is a variant of cordial labeling. In this paper, we investigate 3-Total Super Sum Cordial labeling. This labeling is discussed by applying union operation on some of the graphs. A vertex labeling is assigned as a whole number within the range. For each edge of the graph, assign the label, according to some definite rule, defined for the investigated labeling. Any graph which satisfies 3-Total Super Sum Cordial labeling is known as the 3-Total Super Sum Cordial graphs. Here, we prove that some of the graphs like the union of Cycle and Path graphs, the union of Cycle and Complete Bipartite graph and the union of Path and Complete Bipartite graph satisfy the investigated labeling and hence are called the 3-Total Super Sum Cordial graphs

Pelabelan Prime Cordial Pada Beberapa Graf Yang Terkait Dengan Graf Sikel

Prime cordial labeling of a graph is a bijective mapping of the set vertex to the set where is the number of vertex . The edge labeling induced the vertex labeling, which is obtained by finding the great common divisor (gcd) of the label of vertex which it\u27s adjacent. If gcd of the adjacent vertex label is 1 then the label of edge is 1, but if gcd of the adjacent vertex label value other than 1 then the label of edge is 0, and the absolute value of the difference between the number of edges labeled 0 and the number of edges labeled 1 is less than equal with 1. A graph admits prime cordial labeling is called prime cordial graph. In this paper, we study about edge duplication cycle graph (except for ), vertex duplication cycle graph , path union union of cycle the graph and friendship graph one point union of copies of cycle

4-Prime cordiality of some cycle related graphs

Recently three prime cordial labeling behavior of path, cycle, complete graph, wheel, comb, subdivison of a star, bistar, double comb, corona of tree with a vertex, crown, olive tree and other standard graphs were studied. Also four prime cordial labeling behavior of complete graph, book, flower were studied. In this paper, we investigate the four prime cordial labeling behavior of corona of wheel, gear, double cone, helm, closed helm, butterfly graph, and friendship graph