GRAPH THEORY
GRAPH THEORY DEFINITION A graph G = (V, E) consists of a non-empty set V, called the set of vertices (points, nodes) and a set of ordered or unordered pairs of elements of V, called the edges E set (links), such that there is a mapping from the set E to the set of ordered or unordered pairs of elements of V. Example In the first graph, V = { A , B , C , D } E = {(A,B) , (A,C) , (A,D), (B,C), (B,D) , (C,D)} In the second graph, V = { E, F, G } E = {(F,E) , (E,G) , (G,F)} If an edge e ∈ E is associated with an ordered pair (u,v) or an unordered pair (u,v), where u,v ∈ V, then e is said to connect or join the nodes u and v. The edge e that connects the nodes u and v is said to be incident on each of the nodes. The pair of each node that is connected by an edge is called adjacent nodes . Isolated Nodes If any node has no edges connected with any other node then its degree will be zero(0) and it will be called as isolated node. Adjacent Nodes Her...