W. B. Vasantha Kandasamy, Florentin Smarandache
In this book authors for the first time introduce the notion of subset vertex graph using the vertex set as the subset of the power set P(S), S is assumed in this book to be finite; however it can be finite or infinite. Theey have defined two types of subset vertex graphs, one is directed and the other one is not directed. The most important fact which must be kept in record is that for a given set of vertices there exists one and only one subset vertex graph be it of type I or type II. Several important and innovative features of these graphs are defined, described and developed in this book. The set S considered can be real or complex or indeterminate or dual numbers depending on the problem in hand. However by the definitions of the subset vertex graphs of type I and type II the edges or relation between two vertices are always real. Based on the property that in case of subset vertex graphs for a given set of vertices the graph is unique, these graphs are well suited for social networking. This is one of the special features enjoyed by these subset vertex graphs. The applications of these new types of subset vertex graphs are dealt in chapter three of this book. Authors suggest several open problems for any researcher. Finally these new types of subset vertex graphs will be very useful in general to researchers in computer networks and in particular to researchers in social information networks.
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