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3.3

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 Trees >> rules :-  If a graph G there is one and only one path between each pair of vertices G is a tree. A graph is a tree if and only if it a minimal connected. >> Directed trees :- tress having indegree 1 and no outdegree are called external , terminal (nodes or vertices) or vertices. the node which has outdegree greater than 1 is called internal node. >> ordered tree :- order is defined. >> Rooted Trees : If a directed tree has exactly one node or vertex called root whose incoming degrees is 0 and all other vertices have incoming degree one, then the tree is called rooted tree. Note: A tree with no nodes is a rooted tree (the empty tree) A single node with no children is a rooted tree. >> path length >> Diff between trees and graphs:- > trees have unique path to each vertex but graphs can have many paths. >in trees there is only one root node but in graphs there is no such thing like root node. >trees don't have loops and self ...
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3.2

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 >> graph is noting but a set of vertices and edges represented by G(V, E) >> Directed graphs:- edges are directed by arrows >> Undirected graphs :- edges are not directed by arrows. >>weighted graphs :- edges have some number >>dregree of vertex :- number of edges incident on vertex (self loop is count as 2) >> Path :- if length of path  = n then n edges and n+1 vertices in path. > simple path :- no repeated vertices,no  multi edges(parallel edges) between 2 vertices. > elementary path :-  no vertices appear more than once. >  Circuit or Closed Path:  path which starts and ends at the same vertex, i.e., v 0 =v n . >  Simple Circuit Path:  The simple circuit is a simple path which is a circuit. >> Pendant Vertex :  vertex with degree 1 Pendant Edge : edge incident on vertex with degreee 1 Odd Vertex :  vertexes having odd degree Even Vertex :  vertexes having even degree Incident...
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