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Pdf for graph theory and trees useful for btech students in every college
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Section 1.4: Graphs and Trees A graph is a set of objects (called vertices or nodes ) and edges between pairs of nodes. Vertices = {Ve, G, S, F, Br, Co, Eq, Pe, Bo,Pa, Ch, A, U} Edges = { {Ve,G}, {Ve,Br}, … }
Br Ve Co Eq Ch Pa Bo Pe
A path from vertex x 0 to xn is a sequence of edges x 0 , x 1 , …, xn, where there is an edge from xi-1 to xi for 1≤i≤n. The length of a path is the number of edges in it. A cycle is a path that begins and ends at the same vertex and has no repeated edges.
Br Ve Co Eq Ch Pa Bo Pe
The sequence Co , Br , G , Ve , Co is a cycle. The sequence S , F , S is not a cycle, since edge { S , F } occurs twice. In-class quiz: What is the longest path from Bo to F with distinct edges and no cylces?
Br Ve Co Eq Ch Pa Bo Pe
The sequence Co , Br , G , Ve , Co is a cycle. The sequence S , F , S is not a cycle, since edge { S , F } occurs twice. In-class quiz: What is the longest path from Bo to F with distinct edges and no cylces? A graph is n-colorable if its vertices can be colored using n different colors such that adjacent vertices have different colors. The chromatic number of a graph is the smallest such n. In-class quiz: What is the chromatic color of this graph? i.e., how many colors does it take to color this graph?
Br Ve Co Eq Ch Pa Bo Pe
A graph traversal starts at some vertex v and visits all vertices without visiting any vertex more than once. (We assume connectedness: all vertices are reachable from v.) Breadth-First Traversal
Br Ve Co Eq Ch Pa Bo Pe
A graph traversal starts at some vertex v and visits all vertices without visiting any vertex more than once. (We assume connectedness: all vertices are reachable from v.) Breadth-First Traversal
Br Ve Co Eq Ch Pa Bo Pe
A graph traversal starts at some vertex v and visits all vertices without visiting any vertex more than once. (We assume connectedness: all vertices are reachable from v.) Breadth-First Traversal
Br Ve Co Eq Ch Pa Bo Pe
In-Class Quiz: Find a breadth-first traversal starting with F. A D
In-Class Quiz: Find a breadth-first traversal starting with F. One answer: F,H,D,G,B,A,E,C In-Class Quiz: Find a breadth-first traversal starting with C. One answer: C,A,E,D,F,B,H,G A D
Depth-First Traversal Start with a vertex v and visit all reachable vertices. Start by going as far as you can. Then backup a little and go down another path as far as possible. Only backup as far as necessary, then try the next path. Example: Start at Ch. Ch S
Br Ve Co Eq Ch Pa Bo Pe
Depth-First Traversal Start with a vertex v and visit all reachable vertices. Start by going as far as you can. Then backup a little and go down another path as far as possible. Only backup as far as necessary, then try the next path. Example: Start at Ch. Ch,Pe,Co,Ve,G,S,F,Br,Eq S
Br Ve Co Eq Ch Pa Bo Pe
Depth-First Traversal Start with a vertex v and visit all reachable vertices. Start by going as far as you can. Then backup a little and go down another path as far as possible. Only backup as far as necessary, then try the next path. Example: Start at Ch. Ch,Pe,Co,Ve,G,S,F,Br,Eq,A,U S
Br Ve Co Eq Ch Pa Bo Pe
In-Class Quiz: Find a depth-first traversal starting a F. A D
In-Class Quiz: Find a depth-first traversal starting a F. One Answer: F,H,G,D,B,A,C,E In-Class Quiz: Find a depth-first traversal starting a E. A D
