Some Fundamentals of Graph Theory

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 degree, d(v), of a vertex v is the number of edges with which it is incident. The set of neighbors, N v), of a vertex v is the set of vertices which are adjacent to v. The degree of a vertex is also the cardinality of its neighbor set. 

A path is a walk with no repeated vertices and its length is equal to the number of edges in the path. Assuming u and v to be vertices, the distance from u to v, written d(u,v), is the minimum length of any path from u to v. 

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