Edge of a graph

Two vertices and Vj of a graph G are adjacent if they are incident with a common edge Bij. Two distinct edges of a graph G are called adjacent if they have at least one vertex in common. 

The vertices and edges of a graph may be used to represent hierarchy in an organization. A graph may also serve as an abstraction of a flow chart in an industrial process. 

Recently, Marrifield and Simmons 92) argued that the total number of the following subsets of the vertices or edges of a graph G ... 

The points are called the vertices, and the lines, the edges of a graph. Examples of graphs are given in Fig. 6. 

It is often convenient to label the vertices and/or the edges of a graph by letters or numbers. Such graphs are called labelled graphs and Gh represent examples of such graphs. The vertex and edge sets of these graphs can be explicitly stated in terms of letters as shown here for G ... 

The respective numbers of vertices and edges of a graph, i.e. the cardinality of its vertex and edge set, will be designated hereafter by ... 

Steiner Tree Minimum cost collection of edges of a graph G N, E) providing a path between vertices in subset S C N Cy = (nonnegative) cost of edge (i, j) e E, i < j. 

Definition 13.14. Let DG be the abstract simplicial complex of all disconnected graphs on n labeled vertices. In other words, the vertices of DGn are all pairs with i < j, i,j [n], i.e., all possible edges of a graph onn labeled vertices and simplices of DG are all collections of edges that form a graph... 

A connection table can be regarded as a graph, a mathematical construct that describes a set of objects, called nodes, and the relationships, called edges, between pairs of objects. In a connection table the atoms and bonds correspond to the nodes and edges of a graph, respectively. Such molecular graphs may... 

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