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. We 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.
subset vertex graph of type I, vertex set, graph theory
Smarandache, Florentin; W.B. Vasantha Kandasamy; and K. Ilanthenral. "Subset Vertex Graphs for Social Networks." (2018). https://digitalrepository.unm.edu/math_fsp/203
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