Vertices Explanation

The basic unit as per which the graphs are made is the node. Techniclly speaking, vertices are indivisible and featureless , however, they could contain extra structure based on the purpose; an example for this is, a semantic mesh is that graph where the vertices depict categories of objects.Here you can see vertices explanation.
Brief Explanation of Vertices Explanation

Two vertices that make the edge would be the endpoints, the edge would be the event to those vertices. Vertex w is adjacent to vertex v in case the graph has an edge. A free set is the one where no two of these are next. However, a a vertex cover can be termed that set of vertices which the graph has endpoint of each edge.
Example of Vertices Explanation

Vertices are similar but not exact as vertices of polyhedra. Here the vertices are that of  the polyhedron, however, polyhedron vertices have an added structure that is not there in theory. In a going to graph, the further star of a node u are outgoing edges. Graph G vertices V plus the set of edges E, the forward star of u can be representaed as:

formula of vertices
Conclusion of Vertices Explanation

A graph can be identified as vertex-transitive if the symmetries it has map any vertex to another. It is vital to distinguish between labelled vertices and the ones that are not.  A former links to additional information which enables the same to be distinguished; one can call two graphs isomorphic only if the connection between their vertices pairs up vertices with equal labels. The latter is single and could be substituted for any other vertex based only on its adjacencies inside the graph and not on extra information.